Beautiful dog, glad she survived! Congrats!
Its quite a big damage, as i can see in the in picture. There are some red/black cables also cutted, 1 should be the fan for the printhead and the other for the cooling for fan for the prints. Open the electronic box of the printer and ring them with a multimeter to identify witch is witch.
In the picture you are holding is the main power wire(white,green and black), nice cut(chew)?
If you have a dog or child I really suggest to install a Residual current circuit breaker into your electric box(where are the rest of the brakers are), it senses if there is any shorts in the electric network and cuts power really fast so it prevents electric shock.
Few years ago had a bunny(she was white with huge red eyes) who lived inside the house for a few month until we find a place for her. The garden was owned by a huge German Shepard who was really interested to have a bunny dinner so the only option was to keep the rabbit inside the house, we had a young kitty also that time, so the bunny and kitty become friends and played all day… basically ruined the house…broken vases, killed flowers etc… The bunny loved to chew all the cables for the computer and this breaker saved her life for sure.