To gradually break up with a person over a drawn out period of time because you aren't man/woman enough to just pull the trigger.
"Oh man, I feel really bad for Dara. I got a feelin' Paul's givin' her the slow dump!"
1. It can mean a slow breaking up process as described above. But my first thought on it would be that a slow dump is one of physical bowel constipation. I guess the two of them can be the same, either way you get crap, neither one is pleasurable, both are painful, you hurt before, while, and after it's going on, and they both stink!
I was broke last week, and all I had left in food stamps was enough to buy bread and peanut butter; man was I stuck with the slow dumps all week. I will NEVER do that again! I am gunna but some greens & beans or something next month; this last week jiss about killed me. Thank God it's almost my food stamp pay day!