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If you say "which" instead of "what" or make a similar mistake that doesn't change the meaning or the rhythm, don't panic. Just keep the performance going without interruption. The audience has either noticed or is getting confused, so don't try to fool them by rushing past. You don't need to overreact: just pause and go back to the beginning of the line, or wherever you think makes the most sense. "Bigger mistakes" include saying the lines out of order, forgetting the next line, or messing up the words enough that the meaning or rhythm is affected. Sometimes, your own anxiety can get in the way of your memory. If you've backtracked a couple lines and still can't remember how the poem continues, go back to the beginning. The rhythm of reciting your memorized lines can often carry you through the part you thought you'd forgotten.  For especially long poems, go back a few verses, or about 10 lines. Keep a copy of the poem in your pocket in case you still can't remember the next line. If you don't have a copy of the poem and still can't remember the next line, skip to a line you do know. If you forget the rest of the poem, calmly thank the audience as though you reached the end. The audience at a poetry performance is there to listen to one person perform, not an argument. Anyone who tries to interrupt you should be dealt with quickly by the audience or by the people in charge. Depending on how close you are to the beginning of the poem, you could start again or just go back to a natural starting point a few lines ago. Making mistakes on stage can actually make you a more confident performer in the long run. The dread of messing up is almost always worse than what actually happens. Look back on it once you've calmed down and realize that people will forget the incident sooner than you think.
Keep going if you make a minor wording mistake. If you make a bigger mistake, pause and repeat the last line or two. Take a deep breath and start from the beginning if you completely forget the next line. If someone tries to talk over you, stop until the interruption is dealt with. Realize the mistake wasn't as big a disaster as you thought.