depending on your setup, you might be able to use transform constraints to get what you're after.
It might not be applicable to your setup, but I've created an example with three stem parts. Each part uses an image that can be tiled. The three parts are kept together using two transform constraints. When the stem is sliced, the transform constraint Mix
values are set to 0. You can see it in action in Animate mode.
The setup is pretty self explanatory, but please let me know if you are unsure about anything.
stem-example.zip