The title gives the key. A xenograft is a transplant from one species to another, and the first line tells us the speaker has a pig's heart inside them. The odd image of dining "with" that heart makes it feel like a companion at the table, something foreign but now intimate. The speaker takes it with them to "hell" and to "Mother Rum's," which sounds like a bar or a boozy refuge. Those places suggest a life pulled between suffering and indulgence, and the heart seems to go along for all of it.
The last two lines turn strange and tender. Telling the left hand to "go home and be pretty again" could be a wry plea for the body to return to normal, or to feel like itself. The left side is where the heart sits, so the hand may stand in for the whole altered self. The mood is darkly funny, uneasy, and a little weary. The speaker seems to accept the strangeness, but still wants to feel whole.