The rule (emphasis mine):
"Each poet gets three minutes (plus a ten-second grace period) to read one poem. If the poet goes over time, points will be deducted from the total score."
As Jesster noted, each venue can have its own rules. Some venues have no time limits, some may allow multiple poems. I was in a slam last summer where a poet forgot his poem halfway through and clearly started another. Being one to discuss it (usually here, months later) than file a protest, I said nothing... though I thought that was a clear violation of the rules and the poet should've received a zero or been disqualified altogether...
... but many slams operate from rules that were passed down via oral tradition, and not having a written copy of venue-specific rules on the premises tends to be the rule rather than the exception, so a protest is often not possible.
I've seen this kind of confusion happen when a poet has a long scripted pause in their work. Our slam is in a gallery, with a lot of walls and curtains, allowing for a lot of improvisation. I can hear the beep of the stopwatch clicking back on when the poet starts again, which means they may have gotten 20 extra seconds. This is also commonplace when a poet forgets their poem and struggles to remember it. Do we keep the stopwatch going while they smiled at the ceiling? Heck, yeah.
My guideline to myself is to pass a note to the host if there's something unusual about my poem. I have a few that stop on dimes and a few loong pauses, so I'll let the host or timekeeper (often the same person) know about these in advance to avoid any confusion.
Also, if the person doesn't know the rules, wasn't listening to the m.c. spiel at the opening of the show and tries to do two pieces or worse (time to embarrass pre-SlamRichmond Richmond, VA) recite, word-for-word, a Kanye West rap dressed as Mr. West, they should learn that you will receive applause and be disqualified, not receive a score and a second-place finish. (My hometown has come a long way since.)
Anticipating Rev. BillMac: The time limit is three minutes, not 3:10. The 10 seconds are a grace period.