If you're making a regular cake, you add all the first ingredients (eggs, butter, sugar, ...) and mix everything well. When you add the last ingredient, the flour, you mix until it's just incorporated, since over-mixing can make the gluten form and you'll end up with a tough cake.  If you work with gluten-free flour, can you mix as long as you want? 
If there's leavening in the cake (baking soda or baking powder) that gets activated once incorporated with the rest of the ingredients, and you substantially overmix, you may lose some of its power as you help the gas escape from your batter. Unless you're whipping it vigorously, you're not going to be bringing enough air into the batter to make up for it. This is pretty much like letting the batter sit out on the counter for a while before baking, except faster. 