Complete rubbish. Police are all over the vet clinic looking at the 10 cameras they have. She's half naked. Once you cut the artery (or jugular) in your neck, you will die.
Take all this into account and explain to me how it went from there into an abandoned warehouse with nobody in prison or dead.
It has to be the laziest twist since we found out willy wonky didn't need a cane.
I love willy wonky though.
Do you realize how deep you have to slice through the trachea to get to the jugulars and carotids? Not only does it take a lot of strength to cut through the trachea, but she would have to start in a stabbing motion on one side. The superficial cut, like she made, would bleed, cause pain, and probably shock him, but would not kill him. That is how he is able to survive.
As for the cameras, there would most likely be exterior cameras that are antiquated, and someone who works there would most likely know where the footage is stored. Not to mention the fact that most data will erase itself after a certain amount of time. Animal shelters are not exactly rife with theft. They practically give the animals away for free.