In the Marvel Universe, not explicitly. For example, we don't see the X-Men running around with bags of spare Wolverine or Deadpool blood for its healing effects (although technically they could harvest organs from them). It has been done elsewhere - Heroes allowed Claire's blood to be used as healing factors for others, and DC's Deathstroke & Midnighter can share their blood to give healing for brief periods of time.
Likewise, we commonly see psychic characters either not needing their physical bodies or losing their powers without harm to those bodies. Jean Grey in the Phoenix Saga (comics) has those powers psychically removed, while in the much-maligned X-Men Last Stand movie, Professor X can inhabit the body of his brain-dead twin brother after his body's death.
But the main thing that proves it wrong is the House of M/Decimation Storyline. Here, the Scarlet Witch removed the Mutations by altering reality with "no more mutants" (save about 200) and removing the "X-gene" from them. However, this did not always remove ALL of the effects of the mutation, leaving some depowered mutants still looking like mutants even though their biological cause for that mutation was gone.