The new branches are growing from the rootstock. You will need to cut them off so the rootstock does not overtake your tangerine tree. Look for the graft line and cut any branches off that are growing from below it. It looks like from your picture that the three lighter colored limbs are rootstock.

Cory

You have sour orange rootstock; and those new shoots are from there. Unless you particularly like sour oranges, I would cut them off at the ground and watch for new sprouts. The rootstock "suckers" are only stealing energy from your mandarin ("tangerine")

Thank you both so much for your help. I'm going take your advice and cut those three shoots off. One last question; I live in Jacksonville, FL. Is it too early to trim back the entire tree?

Citrus can be pruned almost any time and to any shape you like.