Can I substitute canned pumpkin for 6 Tbs of butter in a muffin mix (bought)? What ratio? The mix also requires 1 egg and 3/4 cup of milk, would I need to change those?
I suspect this idea comes from the fact that you can, without horrible results, sometimes substitute apple sauce for the butter or oil in some quick breads or muffins. For an explanation on why this works with apple sauce, see Aaronut's excellent answer here:
Like apples, pumpkin is fairly high in pectin (and furthermore, it is variety of pectin with extremely good gelling qualities). Therefore, pumpkin is likely to work as well as apple sauce for this type of substitution (which in my mind is not that well, but that is a decision for the baker....)
Unfortunately, as Aaronut points out in his answer, there isn't really any way to prescribe a precise substitution ratio. It would require experimenting with the amount of liquid (perhaps reducing the milk) and the amount of pumpkin. Trying to replace only part of the fat instead of all of it would likely be far more successful.
So, while with some effort, you are not likely to have a horrible result, but it won't have the same quality as making the mix according to its directions with butter or oil. Of course, it also will taste strongly of pumpkin, which is a much more assertive flavor than apple.
Depending on why you want to reduce the butter, there are a couple of alternatives to consider, based on the fact that most muffin recipes (and mixes) are quite tolerant of changes in some of the ratios (which is also why the applesauce/pumpkin substitution is possible).
If you simply want to reduce the fat (and calories) in your muffins, try cutting the butter by 1/2 or so. The muffins likely will not be quite as delicious, but should still turn out fairly okay.
If you are trying to avoid specifically the dairy fat, substituting a neutrally flavored vegetable oil of your choice 1:1 should work fairly well, although you lose the flavor of the butter.