Your puppy dog probably has a sarcoma. Maybe Hemangiopericytoma, or Fibrosarcoma sounds familiar?
Ask your Vet about local radiation at the site. Frequently that's used to help clean up the margins of the incision earlier before the cancer has a chance to penetrate the deeper layers. Whether it stays localized or undergoes any metastasis depends on the pathology report. But again, radiation might be a helpful short term treatment. Depending on the exact type of cancer, possibly Chemotherapy is an option. Although sarcomas are difficult to treat.
The only thing you should be concerned about per diet is to stay away from carbohydrates and especially sugar. Cancers in general due to their higher metabolism will preferentially use sugar-->other complex carbohydrates-->proteins in the diet. They seem to have a difficult time utilizing fat in the diet. In general a high quality commercial dog food will do as well as any other diet for a cancer puppy.
The only supplement that may help which has research to back it up is fish oil due to the Omega-3s. The Omega-3s will normalize lactic acid levels (by-product of cancer metabolism of sugars). It can act to slow down cancers through a weak anti-angiogenesis (prevent blood vessel development), and also has weak anti-inflamatory effects. Do not use flax oil. Besides a low conversion rate to long chain Omega-3s that can be utilized, a part of it may be converted to long chain Omega-6 fatty acids which have been shown to promote cancer growth.
Anti-oxidants probably won't help much, but they won't hurt either. The only herb that I'm aware of that has shown some anti-cancer properties and has some scientific studies to back it up is Artemesin. Unfortunately it's in great demand due to its anti-malarial properties in humans, and surprise carries a hefty price tag. So beware of Internet sites which sell Artemesin at cheap prices, the purity is likely suspect.