Why does the pasta I make with my extruder always stick together?
Your dough is too wet.

Four eggs is a lot for 2 cups flour - the KPEXTA user guide suggests 4 eggs + 1 tbsp water for 3-1/2 cups flour. Assuming you're using the mixer to mix the dough, it should be crumbly and not form a ball, but it should hold together when you pick some up and squeeze it in your hand. If you have a kitchen scale handy a typical egg pasta ratio is one large egg (about 1/4 cup) per 100 grams flour.