For the cake we needed melted chocolate with some extra sugar.
However, instead of sugar we have added salt.
Is there a viable way to separate the salt?
The chocolate has 60% cocoa in it, and there's also some butter in the mixture.
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You might be able to draw off some of the salt with water if you're very careful, since neither cocoa solids nor cocoa butter are really that water soluble. It's very tricky though, and if it even works it may take a lot of effort - if you let the water and chocolate mix it won't work, an emulsion with the saltwater mixed in instead of separating out will have no way to get the saltwater back out of your chocolate. Even if you do it right there's no way to measure how much salt is dissolved out of the chocolate in each attempt since that will depend on the concentrations, temperature, and texture of your chocolate - so be prepared to experiment. The whole process is Not Recommended if you need pure chocolate, by the way, since the end result is a thick moist chocolate paste, but OP mentioned it is for a cake, so it might be worth trying. If you don't think its worth the risk and extra effort, you can skip to the bottom of my answer and use up the chocolate over several recipes by omitting the salt in them.
If you want to try it, melt your chocolate gently, spread it out thin as you can in an extra-wide container (lots of surface area), and when cooled to at least a semi-solid layer, gently pour water over the top (warm might help, but cool is also fine) - your chocolate really needs to be cool and sturdy enough the pouring doesn't mix the two. Ideally, you want a layer of water over a thin layer of chocolate. Let it sit for a while, maybe taste the water to confirm salt is being pulled out. Over time, the salt should be pulled off the surface layers into the water, and the chocolate should absorb water - the warmer your chocolate and water are, the quicker this will happen (since there's more motion in both), but you'll probably have most of the surface salt dissolved within an hour or two.
You can get a little more salt out by breaking up your (by now, cool and solid) chocolate and let it sit in the water for a while, exposing more surface area. When you think you might be done, scrape a little tasting sample off the chocolate to taste if the salt is still noticeable on the surface layer, let it sit longer if it is. Carefully pour off the water (chilling might help if your chocolate got soft in the water), pat dry your chocolate, and take a sample out of the center of a piece of your chocolate to see how much salt is left. It will still be salty, since the under layers aren't getting the salt pulled out like the surface, and it will be wetter from the added water - but a few repetitions will hopefully pull the salt level down to acceptable without losing much chocolate flavor.
When remelting your chocolate (for round two, or for the next step in your recipe), you need to be careful so the chocolate doesn't seize. Melt your chocolate into a little bit of water - maybe a tablespoon, to start with, and a small container of hot water on hand so you can add a teaspoon anytime it looks like it might be misbehaving. You might need up to 20% water (by weight) to keep the chocolate smooth, depending on other ingredients. Obviously, this is not much of a problem if you're planning on adding other liquid ingredients, like for a batter or sauce, but might be trickier if your recipe was for a ganache or frosting where the extra water might end up substituting for other moist ingredients. Or you can actually try melting the chocolate into those wet ingredients, but some of the flavor is likely to be pulled off into the water if you're doing another round of drawing out the salt, so maybe only do this if you're sure it is ready for your recipe.
If you're pulling salt a second time, spread the chocolate out into your wide container, and cool until firm - it will be wetter, and you need the layers not to mix. Ideally, you're working with a soft chocolate or fudge-like texture, rather than something more goopy. Let it sit under water for a few hours or so. The extra water in the chocolate layer will let the salt escape a lot more easily, and also sugar, but it will also make surface layers of your chocolate much softer with added water in direct proportion. If your chocolate is sturdy enough, you might want to break the layer up again to increase the surface area. Chill thoroughly before pouring the water off - you may lose a bit of chocolate if the very surface diluted to liquid, so be careful. You will not need extra water melting it for the third time, you may actually wish to heat it a little longer in the hopes of evaporating some of the extra water off.
Taste the chocolate when it's melted again. If it still tastes very salty, repeat the layering-with-water process until you are satisfied. If it is salty but reasonably edible, you might consider if there's salt elsewhere in the recipe you can lose, or if you would be fine with a salted-chocolate recipe (think salted caramel, it will be different but might be good anyway). You will need to add sugar to your chocolate before it can be used, not just for your original recipe, but also because the process draws sugar off along with the salt (as both are water-soluble) - so keep that, and any other ingredients in mind when figuring out how much the salt taste is going to be diluted in the end result. I would not recommend using it in a recipe unless you're fine with the balance of tastes in the undiluted salty-chocolate, though, because the salt will be diluted at the same rate as your chocolate, it won't go away.
When working with the results of this process, you will need to be careful when figuring out how to compensate. The extra liquid might mean your product is looser, or that you use less of another liquid to reach your desired consistency - or you may need to heat longer, to evaporate out water (and replace with more flavorful liquids, like milk or cream) if your recipe needed a drier consistency and you don't want to lose the richness. You will need to taste often, to figure out if you need to balance flavorings, if you need extra sugar, if the salt is still to noticeable (if it is only a bit, you might try to dilute the recipe and deal with leftovers). It will be a lot more reactive and intuitive, not following the recipe so closely.
For an easier and much more simple option, you can use the chocolate up over several recipes. Look for salt elsewhere in your recipe, that the salt in your salty chocolate can replace. Lots of baked goods have some salt in them, though probably not as much as you've added - again, this is easier if you're using it in a batter where the salt will be present, rather than trying to balance across different parts of a dish, under-salting a cake to try to balance a frosting or ganache might not work. You can get the right salt level in the overall recipe by using some of your chocolate (measuring by amount of salt per amount of chocolate), and adding in fresh chocolate for the rest - using the leftover salty chocolate in other dishes. It may take several recipes to use up your chocolate, depending on the amount of salt involved, but the chocolate won't be wasted - and you might try out some savory dishes with a bit of chocolate flavor, as well as chocolate dishes with a bit of salt.
You can even use both techniques, reducing or omitting the salt added elsewhere will give you a bit more wiggle room for how much salt you can easily pull from the chocolate (spreading the less-salty chocolate over fewer recipes) - though in that case, you will need to taste carefully, since the results are harder to measure.
Since chocolate does not boil (to my knowledge) you could not use distillation.
Chocolate is oil based which is not polar so salt has a low solubility.
Salt is very soluble in water. You could remove it via dialysis (osmotic pressure). Basically salt likes water more than chocolate.
This is a reach. Chocolate and water are not soluble. Melt the chocolate with like 5x the volume of water on the stove just hot enough to melt the chocolate. Stir very lightly for like 10 minutes. If it forms an emulsion this will not work. Cool in fridge for the chocolate to solidefy. Pour off the water. Hopefully the water extracted enough salt. It will also extract some sugar (if it works).