>>1021645
The way I would do it is:
- Select all the edges you want to cut, then right click and choose subdivide.
- Add a plane (can be in the object or a separate object) and align it to the grid line you want the vertices to snap to.
- Turn on vertex snapping (face), select the vertices you created, and double press g to slide them to the plane. You may have to slide them individually because slide doesn't always like to behave.