A "suppository" is a medicinal capsule generally inserted into one's anus, though for women, it can also refer to inserting it into the vagina.
Therefore, in slang, the transitive verb "supposit" is a round about way, or maybe euphemistic way, of saying "shove it up your ass" (see def. 8). This is a vulgar expression one says in contempt, albeit sometimes sarcastic contempt, and can be specific to a real item that is being referred to as "it" or in replacement of "it" but very often simply uses "it" intangibly to loosely refer to everything the person it's being said to just said, their opinion, or even the entire disagreement or situation.
"Thanks for your input, but why don't you supposit it?"
"You want your money? Well, here's your money. Now go and supposit it!"
"Oh, so I'm not good enough for you? Supposit it!"