Mandevillas do like to be pot-bound. Half of the potting soil needs to be removed and new soil added. In April or May, start fertilizing weekly - they don't like to be soggy, either. You should cut it back to about a foot and treat it for spider mites. You should see new growth in March or April. You can move it outdoors in full sun in May.

You can do as kavjones suggest or simply repot it one or two size larger. This way you don't disturb the roots at all. I have a Madevilla that is over 20 years old which I bought from a mail order company. What I received looked like a stick in a small pot. But I gave it 2 years in that pot until it was big enough to go to a larger size pot (1 size up). I did that every two years and it's now in a huge pot the size that holds a tree. It's just in time to make the move with me to Florida where I plan to permanently plant it against a trellis.