Technically, yes.
Realistically, however, you are going to break far more than is worth it trying to get to the part to replace it.
The Mini DisplayPort socket is soldered directly onto the motherboard, so if you were to replace it, you would likely need to replace the whole motherboard. (Unless yours is a purely mechanical problem, in which case a new socket could be soldered to the motherboard as a replacement.)
The real problem lies with the initial opening of the device, however, as unless you are already experienced in removing this type of screen, you *will* break it while removing it. You also stand a very good chance of mangling your WiFi antennas while you are at it.
For most, the Surface 3 is simply not a repairable device. Many of the design decisions made to allow for the extremely light and thin tablet have made it so that opening the device once it has been made is an exercise in frustration. A well equipped repairman with the right tools, skills, and direct experience with Surface 3 repairs could replace the part and return the tablet to you intact, but it would likely be expensive.
Sorry for the bad news,
Harold