Laser diodes run stupidly high intracavity power levels, and you will case optical damage to the laser diode itself if you try pulsing a nominally CW diode.
There are such things as "Quasi CW" laser diodes, which really means pulsed diode with enough cooling that you can get a reasonable PRF.
Then there are explicitly pulsed diodes, these have low gain so you need a lot of current to get to threshold, and thus cannot be run CW, but they do manage reasonable peak power levels. Pulse forming networks are key to getting these to work properly.
What you usually want for ablation is a Q Switched laser, but seriously dangerous to vision in many cases. Were I doing it I would probably be reaching for a fibre diode laser from someone like ILP which are available in a Q Switched variant, and are an easy to operate self contained package that usually runs at somewhere in the 1um wavelength region.
The laser engineering on its own is a nice grad student project, never mind doing the micromachining once you have the miserable thing. If the machining is the interesting part then I would buy the source in.
Do talk to your institutes laser safety people, not only are they generally knowledgeable folks, but they know where the lasers that the university already has are hiding, using something that some previous research used is good for your budget....