Yes. Why would you want to leave it?

Mike

Definitely prune the shoot. Also, did you just plant your tree? It shouldn't be dropping it's leaves like that unless recently transplanted. These trees are really finicky as a fresh planting and need tons of water the first year and a decent amount the second year. Anyway, cutting this limb off will also take some of the stress off the root system trying to provide moisture for the leaves on it.

Yeah I planted mine in the fall of '12 and the next spring it leafed out great but shortly after that it lost about a 1/3 of its leaves. I trimmed back a few branches that I would have eventually anyway and made sure it was watered very well. Don't expect much out of it this year. Also, mine has only grown about 6-9" the last two years. It's still rooting and callousing over some nursery wounds.