What do you do if you are a Christian and you don't want to exact revenge on the "annoying agitators" e.g. mocking, imitating, etc. E.g. you do something that you typically do, then almost immediately after you do it, the "annoying agitator" mocks you by imitating you and making fun of you.

Matthew 5:10
Blessed are those who are persecuted for righteousness' sake, For theirs is the kingdom of heaven.
Matthew 5:9-11 (in Context) Matthew 5 (Whole Chapter)
Matthew 5:12
Rejoice and be exceedingly glad, for great is your reward in heaven, for so they persecuted the prophets who were before you.
Matthew 5:11-13

Praise God that you are counted amongst those who are persecuted as well! And pray for those that mock you. Ignore them and walk away.

Being made fun of is persecution. You are not accepted for who you are and mocking someone is persecution.
2 Chronicles 36:16
But they mocked the messengers of God, despised His words, and scoffed at His prophets, until the wrath of the LORD arose against His people, till there was no remedy.

Matthew 27:31
And when they had mocked Him, they took the robe off Him, put His own clothes on Him, and led Him away to be crucified.

I basically laugh back. If they see they can't get to you then what is the use of their trying and they will give up eventually.
The last thing you want to do is let them know it upsets you because that is the reaction they want!

You just go on, most make fun of you since they feel more insecure than you and make thierself feel better by making others feel bad.
If you ignore them, it may help, and at worst, you just ignore them.

savedsinner7, I understand what you mean by persecution and all that. But that is still not what I'm talking about.

What do you mean then? Help me understand.
savedsinner7, I understand what you mean by persecution and all that. But that is still not what I'm talking about.

I agree with fr_chuck. Just ignore them. They are just doing it to get a rise out of you, if they think it doesn't bother you then they will move on and agitate someone else.