I’d say it’s possible to forgive in the sense of repairing the relationship even if the offender is also punished for the act. It does probably help if the punishment is something automatic done by a third party (usually the authorities) rather than something inflicted personally by the supposedly forgiving person, though.
As a famous Catholic example, St. Maria Goretti forgave her murderer before she died and (according to his testimony) appeared to him from Heaven to say she was praying for him to repent and join her there. It took awhile longer, but even Maria’s mother chose to forgive and even befriend the young man. Nevertheless, he still spent time in prison for murdering someone. (He does seem to have gotten out awfully early for a murderer, perhaps because he was young himself when he committed the act, but I don’t know if Maria’s family had anything to do with that.)
Usually, victims have little control over the state’s punishment of a criminal, though they may be able to Influence the length of a sentence in either direction. I have heard of victims or victims’ families actively lobbying against particularly extreme and permanent punishments, such as death or the blinding you mention.
I also don’t think that the Christian expectation of forgiveness takes away from our ability to do so, as long as it is recognized that we are going beyond what we are owed in justice (so that the offender or society at large shouldn’t be able to guilt someone into forgiving as though it’s the only civilized response).