It's not clear from the article excerpt that this was a marine sea turtle. Probably a large snapper as these inhabit the lakes around here in Daytona. Regardless, it is cruel and unnecessary to torture and brutalize any animal. Kudos to the vet for taking action to protect the turtle from these three viscous animals.
I used to catch large snappers with my uncle. Never cruel - although you did need to kill them before you cooked them. My uncle's method was to hold a pliers in one hand and have the turtle snap at your outstretched hand - and then grab him by the lower jaw with the pliers. Then with the sharp knife in your other hand you would cut his head off, starting at the bottom of the neck. I think that is about as clean and quick as one could do it.
I know that I was probably more scared than those turtles. Me with the pliers having a 15 pound snapper chasing me backwards around his patio! “Come-on just GRAB his jaw. DON'T drop the pliers. Okay I got them, now here - just DO it!” (I'm glad that was back in the day before i-phones, it was sure comical looking back).