Install the addon and activate Mesh Looptools internal addon. This one is seriously recommanded. The generated mesh will be better.

Switch to orthographic view (numpad5)

Follow the steps in the dynamic help. So first use DRAW CUTTER button

Draw the spline then hit TAB when done. This switch from spline edit mode to object mode.

Press MESH CUTTER button to generate the CUTTER from the spline. Check if the CUTTER go through the object(s). If not, scale it and move it. The best is to scale it and move it in is local Z axis so the cut will still be at the place you draw it. Use shortcut SZZ to scale it in local Z and GZZ to move it in local Z.

Select the object(s) then use CUT button. You can select the CUTTER with the object(s), not a problem.

Done. you can see here a shading problem with blurred stain. This can occured on curved mesh. You can correct this by adjusting its normals autosmooth settings.

Some cuts will generate more than 2 parts.

one of the parts here have to be separated. Use the Split button for this. You can recenter Origin to geometry with the Origin button.

There is 2 displace options for the CUTTER mesh: Noise and Texture.

Both of it have its own settings based on scale, strenght, details... Test the best displace then Cut when it's OK for you. A bunch of tilable textures are delivered with the addon but you can use your own. 

Material:

A material is generated for cuts shading. By default its mapped with a checker. Don't forget to apply a material on yous object before to cut. If not, the cut material will be applied on the entire object. You can named a existing material in the Cutter Material section. The addon check if this name allready axist and apply it. if not, it create a new one with a checker.