As a word, swearapeutic has its good points: for one thing it's easy to guess what it means (that is, the feeling of release that swearing sometimes provides), and for a second thing it allows us to express a useful concept in a single word.
But, having said that, it's still utterly and irredeemably hideous, isn't it.
Sunday Rest: swearapeutic. Word Not To Use Today. This word is, obviously, a mixture of swear and therapeutic. It started off conveying the idea that swearing can be so useful it can take the place of therapy.
Swear comes from the Old English swerian (yes, we've been swearing for a lot longer than we've been having therapy) and therapy is from the Greek therapeia, attendance.