well im no expert in modeling but here are a few things that may help.
as far as i know there is no tool that will directly project a curve onto a poly surface.
but you may consider a sort of boolean operation where you can cut a poly surface with another poly surface. Booleans can be tricky for beginners especially if you don't understand them very well.
there is also a tool by JT I think its called JT_poly_Stencil that will do sort of the same thing as boolean... it will allow you to intersect two surfaces and the then a new poly face/division is made where the surfaces intersect one another.
and my last tip is to line up your curve with the poly you want to slice and then turn the cv's on the curve. then use the split poly tool and you can snap the tool to each vert. this can be tedious and doesnt quite give the same results but can be good to rough something in.
best of luck