Can you play Mind Rape on a tapped vampire?

Mind Rape

Tap a younger vampire and put this card on that vampire; you still control this card. This vampire does not untap as normal. During your next minion phase, burn this card to untap this vampire and take control of him or her until the end of your turn.

Yes, you are always allowed to try to tap something tapped, except the card tells you otherwise, for example ...

Mind wrote:

  Put this card on any untapped vampire. Tap that vampire; he or she does not untap as normal during his or her controller's untap phase. Burn this card during your next untap phase.

 As above, with +1 stealth.

Hakuron wrote:

Yes, you are always allowed to try to tap something tapped, except the card tells you otherwise, for example ...

Mind wrote:

  Put this card on any untapped vampire. Tap that vampire; he or she does not untap as normal during his or her controller's untap phase. Burn this card during your next untap phase.

 As above, with +1 stealth.

Partially correct (you cannot tap as a cost something that is tapped (for instance: Carmine Giovanni can't tap herself to give an ally +1 stealth while tapped).

But anyways: Yes, you can play Mind Rape on a tapped vampire, as it taps that vampire as an effect ("Tap that vampire." rather than "Tap that vampire to..").

Follow-up question ...

I successfully play Mind Rape on a vampire (round x).
Before my next minion phase (in round x+1), that vampire goes to torpor.
In the minion phase of round x+1, I successfully play Graverobbing on superior at that vampire in torpor.

Can I then use the effect of Mind Rape to untap the stolen vampire and act with it?

Tap a younger vampire and put this card on that vampire; you still control this card. This vampire does not untap as normal. During your next minion phase, burn this card to untap this vampire and take control of him or her until the end of your turn.

Thanks in advance!

Hakuron wrote:

Can I then use the effect of Mind Rape to untap the stolen vampire and act with it?

Yes; no part of the card text requires the vampire to be controlled by another Methuselah when activating that part of the card text.

The more commonly seen similar situation is using Temptation on your own vampire. You can burn the counters and take control of a vampire you already control, untapping them in the process.

That's not 100% correct. I'll paste Graverobbing's cardtext:

Graverobbing
[Action] Action

[Dominate] Dominate

[dom] Steal a vampire in torpor controlled by another Methuselah.
[DOM] As above, and this acting vampire may burn 2 blood to move the stolen vampire to your ready region.

Since you're in your minion phase, you can trigger the effects as you want, so the correct order should be:

1. Use Graverobbing (since you cannot use it on your own vampires)
2. Do whatever stuff you want to do
3. Burn Mind Rape to untap the stolen vampire, since burning Mind Rape during your minion phase is mandatory (if not you could leave a vampire permanently tapped, like with Sensory Deprivation and the card is not intended to work that way)
4. ...

Is not a matter of if you CAN or NOT burn Mind Rape. You MUST burn Mind Rape during your minion phase.