Back in my childhood, one of the kids in my neighborhood had a 3 legged German shepard which had it's left rear hind leg severed at the knee. It was a fairly large dog, and despite its handicap, adapted quite well. It wasn't able to run and it had difficulties getting up, sometimes needing a pull on the collar, but it got around fine. It simply hopped on its rear foot, while its two front legs had a normal gait. A game of fetch would take a longer to complete, but the dog still enjoyed playing it. Outside of missing one leg, it was every bit the typical household pet. Did the dog have a good life? Absolutely. It was adored by all the kids on the block and it's family.

Your decision should be based on the expected quality of life. I would think that different breeds of dogs have different tolerances to various disabilities. The other factor is whether or not the type of cancer is expected to reoccur and if there is a chance of completely recovery after chemotherapy. A seasoned vet should be able to forecast your rottie's ability to survive this and have a fruitful, productive life.

Good luck to you. I hope your dog can be saved.