They use a small hole punch device after a spray anesthetic on the area to make a pinhole size hole. They pull the vas through and cut it before sheathing the vas so sperm can't get through then do the same with the second vas.
I had a small amount of pain with the second one but they applied more spray. It is kinda my own fault for not telling them ahead of time that I process all anesthetic drugs fast. I don't know why but I always require refreezing at the dentist for regular procedures.
https://www.pollockclinics.com/no-scalpel-vasectomy/our-approach/