Remove Lines outside of clipping mask on complex art?

Hello,

I'm looking for a way to delete hidden lines completely outside of a clipping mask (and/or draw inside), because our cutting software still sees these paths.

1. Desired result

2. Cutter View

I've seen several posts on here about shapebuilder or pathfinder cropping, but neither of those options work. I'm using Cutting Master 4 in Illustrator 2024