In a Side Scroller Blueprint how would I go about getting the current mouse location and launching a projectile at it?
Mouse event click > get cursor location(probably called something different) > spawn projectile > add in rotation and scale transform vectors and you have yourself an object.
Take a look at the fps tutorial for details on spawning a projectile. Google search some for more results on the subject.
To get a more accurate picture of how you specifically could go about implementing this into a 2D game wed have to know more and is entirely up to the design of the game.