Often in political campaigns a point is reached at which candidates take out their gloves and start slugging with bare fists.
Is it correct to say? Especially the bolded part.
First of all, those round brackets are almost always called parentheses, or specifically round brackets. The phrase within it, is called a parenthetical. They are used more like commas in English. Square brackets would be more appropriate here.
I think the phrase you're looking for is "when the gloves come off". It's an idiom or metaphor which means the contest is now more serious and and the contestants are now looking to hurt each other.
I would use "when" rather than "at which" because a campaign is carried out over a period of time. I would write that sentence like this.
Often in political campaigns a point is reached when the gloves come off.
A similar phrase would be "Not pulling any punches". Often in political campaigns a point is reached when the candidates are not pulling any punches