This whole poem rests on a foundation of wounded, indignant hyperbole. Rejected by his beloved, the speaker tells her that she's no better than a "murd'ress," a female murderer: he'll die of his heartbreak, no doubt about it, and won't she be sorry then?
As Shakespeare's Rosalind once put it: "Men have died from time to time, and worms have eaten them, but not for love." The speaker might feel wretched, but suggesting he's going to actually keel over from his misery is putting things a bit strongly.
His whole revenge plot, however, rests on his faith that he'll die and return as a sinister ghost to haunt his beloved while she lies in bed with another (and "worse") man. The most dreadful part of his visit, he imagines, will be when he says terrible words to his one-time beloved—words so terrible, in fact, that he won't even warn her what they are now, in case she's scared into changing her mind and accepting him. He wouldn't want her now even if she begged him to take her back, he claims.
Again, readers might detect just a sniff of hyperbole here. The speaker clearly still has some feelings for this woman, even if they've taken the form of hatred. His equally hyperbolic claims that he'll die of love and that he doesn't love her anymore at all add up to one darkly funny picture of crazed heartbreak.