Well, there's punishment and there's "punishment". I think if you ask most sane minded fair persons they'd say that punishment would entail having your freedoms curtailed, being removed from society, having access to friends/family/associates controlled and restricted - i.e. loss of liberty.
However during this period of incarceration, prisoners have a right not to be physically and mentally abused by their fellow inmates and jailers. Incarceration is the punishment, not beatings and rapes.
As to the killing of death row prisoners, their punishment involves not just the loss of their liberty, but also their loss of the right to live the remainder of their natural lives. But it does not give the state the right to make participant endure several minutes of deliberate and avoidable excruciating pain whilst being put to death. I'm fairly certain your justice system doesn't codify that kind of barbarism as part of the death sentence.
If The Dignitas Clinic in Switzerland can provide pain free assisted suicides then surely it's possible to kill death row prisoners just as humanely in the US.