First of all, I have no experience with lasers.

Is there a cheap laser (~150EUR) that can cut 10cm thick XPS?

AFAIK, there are two types of lasers: laser-diodes and real-lasers.

I guess real-lasers would cut XPS with no problem but are expensive.

Are laser-diodes strong enough to cut XPS?

I understand that laser-diodes are better suited for engraving,
because of focus problems, right? If I would somehow change the
focus dynamically, would it then cut 10cm of XPS? At what speed?

Thank you.