mmadsen said:
But it was also impermissable to maim a fellow Muslim. In fact, the Islamic nations for a long time relied on wars against Christian nations to supply eunuch slaves. They also filled their armies with elite units of enslaved Christian orphans.
Mostly right.
Eunuchs were taken from non-Muslim populations because, first and foremost, they were to be enslaved, and Muslims were forbidden from enslaving Muslims, without exception. (doesn't mean it didn't happen, of course, just that it was forbidden.)
The maiming issue was secondary for the eunuchs (well, for the people who wanted the eunuchs at least. For the eunuchs themselves ...

)
An ordinary Muslim could not harm another Muslim, nor even a non-Muslim who paid the jizya (poll tax on non-Muslims) and submitted to Muslim rule.(Actual practice varied quite a bit).
However Muslims at the time were permitted to injure a slave if (and only if) there was good cause (ie., justified punishment, meeting the needs of the state [this was how creating eunuchs was justified]). Going beyond this was deemed cruelty, and an person found guilty of cruelty towards a slave could be punished, and have the slave freed.
As for the "cutting off the hand of a thief" penalty, it, and other bodily punishments were allowed, and indeed prescribed, by the Qur'an, for both Muslims and non-Muslims. At first, any Muslim was permitted to carry out the punishment, but as the Islamic judiciary developed in the eighth and ninth centuries, it became for and more common that only a qadi (judge) was allowed to order punishments of any kind, bodily or no.
Enslavement of a Muslim was specifically forbidded under any circumstances, however, (and could not, therefore, be imposed as a punishment) because a Muslim was supposed to be a slave to God alone, not to another human.