To get the "dong arm" means to get screwed over hardcore, to be punished in some way (especially not having studied enough for a test).
Specifically, the meaning refers to a penis beating/dickslapping.
The origin of this phrase was when my roommate threatened to beat me with his penis, then waved his arm threateningly to simulate. He then said, "Yeah, I'll give you the dong arm." A revolution began. Later we agreed that if he didn't go to bed, he would get the "dong arm" on his Physics exam.
See: Derrick Toth on urbandictionary.com