Well, I don't claim to be a Bible scholar, understand the history surrounding the events laid out in Amos 1, but from just looking up the words and putting together meanings, I have two possibilities (both of which could be wrong)
I don't know who or what Gilead is. The name "Gilead" is used in the Bible to reference two places and three people. I don't know which applies here, but each of my two possible answers will assume one of each.
Main Entry: thresh (verb)
1 : to separate seed from (a harvested plant) mechanically; also : to separate (seed) in this way
3 : to strike repeatedly
Sledge has two possible meanings - Sledge, as the shortened form of Sledgehammer, or Sledge, as a Sleigh. I doubt Damascus was riding a sleigh to anger God, so I'm sticking with the sledgehammer with a pointed tip. Think about a meat tenderizer....but much much bigger.
So here comes my two interpretations of the passage. I think the first is more likely to be accurate, but I'll list the second as a possibility as well.
First, it is possible that a man named Gilead was threshed (definition 3 - stricken repeatedly) with sledges (that is, sledgehammers with pointed ends).
The second interpretation is that Damascus (being a territory, an empire) came into Gilead (Gilead means hill of testimony or mound of witness, (Gen. 31:21), a mountainous region east of Jordan) and destroyed it with the same weaponry, separating the people, destroying the land as they went.
If the second is accurate, it would be understandable because at that time, when an empire conquered a new area, they would scatter the people amongst several other territories, so there would be less chance of a revolt. Rome was especially good at this.
Anyway, without going back and reading up a little bit, there are my guesses.