Slice

Create a box and inside the box create a teapot and torus, apply slice to the box from the modifier list, click on the plus sign next to slice and select slice plane. Use the move and rotate tool to drag the slice plane.
To change material with this modifier, I created a sphere and apply a blue material, right click on the sphere and select clone, apply a red material and slice on to the new sphere, click remove bottom from the slice parameters, and use the move tool to drag the slice plane.