My preferred method would be to juice the mint in one of those juicers meant for wheat grass which can get a ton of moisture even from a dryish plant, then use this juice pure or dissolved in sugar.
The second thing you can try is maceration. This is usually done with fruit, and means you cut it up and mix with sugar, then leave to stay for several days. With fruit, lots of juice flows out, but with mint, I'd suggest simply adding a little water. It won't split the cream if the amount is small enough. You'll get an even better extraction if you add a bit of vodka. Make sure that you use enough sugar to not have the stuff go moldy or ferment.
Logophobe's idea for infusing the cream also sounds good. David Lebowski has several herb ice creams which involve transferring the flavor to cream, then discarding the plant matter. He calls for boiling the herbs in the cream, and this works very well - almost too well for me, the sage ice cream turned out to be an acquired taste. The taste changes during cooking, but if that's OK for you, cooking up a sugar syrup with mint, or making a strong mint tisane and then cooking a sugar syrup with it, may turn out to be the easiest way to prepare that. The advantage is that sugar syrup is boiled to supersaturation, so you get no free water afterwards to interfere with your cream whipping.