There is no reliable historical or biblical evidence to support the claim that John the Evangelist had his eyes removed.
Some apocryphal traditions (writings not included in the accepted biblical canon) mention John suffering various tortures, but these accounts are legendary and not considered historically accurate.
The traditional view is that John lived to old age and died of natural causes in Ephesus.
Therefore, the answer is no, there's no reliable evidence that John the Evangelist had his eyes removed.