Firstly, a cat of ours who died recently, Charlie, was abused by her previous owners. We got her as a kitten when I was a baby. She had kittens while I was still a baby, and had an extreme reaction to our retired seeing eye dog's getting too near to her kittens. Despite the saying "fighting like cats and dogs", if a cat and dog are introduced when one or both are puppies/kittens, they will usually not fight. But Charlie attacked our dog, clawing and biting. My dad tried to split them up, and she turned on him and bit his hand, almost chewing off one of his fingers. He still doesn't have full mobility in that finger, 15 years later. Once Charlie calmed down she was very remorseful.
Before I was born my parents had another cat who'd been abused. In particular, she'd had someone try to vacuum her up, permanently damaging her tail. My dad was cuddling her one while my mom started up the vacuum cleaner in the next room. Most cats are a little scared of the vacuum cleaner and will avoid it while it's on, but are fine with it if it's nowhere near them. This cat panicked and tore out of my dad's arms, scratching him up in the process.
One person on the internet was talking about a male pet rat who used to belong to a laboratory. They always picked him up by the tail, a painful thing for a rat. This rat would run away from a person trying to pick him up, and bite if they cornered him. This is unusual for a tame rat. They had to gradually gain his trust before he would allow them to pick him up.
Another person on the internet was caring for a litter of pet wolves who'd been taken from a person who had them illegally. One of them had been thrown over a fence by the scruff of his neck. When she reached to pat him, he immediately recoiled and bared his teeth, a signal to 'back off'. He was unhappy and refused to play with the other pups, spending most of his time hiding in one section of their pen.
There are animal studies going on about PTSD. Here and here and here(PDF) they describe using animal models of PTSD. Also, people with experience taming abused and feral animals say that those who have never had owners are easier to tame than those who've been abused and/or abandoned and then went stray. The feral animals have no idea what humans are like, but the abused ones know about humans and don't like what they know.
In conclusion, although animals most likely have differences in terms of trauma, mammals, and probably other types of animals too, can be traumatised.