Maybe more like, sat up and stuck its head down into the vase, which tipped, startling the cat, who pulled back, lifting the vase, and either thrashed its head or jumped down, either way the body of the vase broke away. It looks like it got lucky and there's a relatively straight break line, but you wouldn't want to pull in case you thrust a jagged shard into a jugular or something. They seem to be at the vet where they'll administer enough anesthetic to either ease it off or break it away, then clean/stitch any cuts and dose it with antibiotics. If you couldn't get to a vet, a couple people could probably wrap it in a towel and hold it still enough to break the vase away but it's risky.