AFAIK, there's no way of trimming Curves natively in Blender, (cutting a spline, and recalculating the parameters to approximate the intact spline.) It can be done outside, at least in Adobe Illustrator, I don't know about others.
Inside Blender, I think you have to go via a mesh representation... something like this...
- In Object Mode, AltC, convert the stock curves to a mesh, and CtrlE > 'Bridge Edge Loops'
- Raise the trimming curve above the mesh in, say, Z..
- In Object mode, select the cutter, then the stock, making it active, put it into Edit Mode.
- Looking down Z, Knife Project the cutter onto the stock, with 'Cut Through' checked.
- In face mode CtrlI invert the selection of faces, and X delete.
- In edge mode, CtrlAlt select a vertical ring of edges, and in the Select header menu , Select Loops > Edge Loops.. check for edges not caught by the loop selection..
- P part a duplicate of the edge selection to a new object, and AltC convert back to a curve.
I may have missed a trick or two.. and would expect your situation to be slightly different anyway...