Shut up, it’s a good title. Anyway, I think it’s weird that cute shows up as a suffix in so many words when it means, well, cute. So why is that? Well, it turns out that cute isn’t even the origin word here—acute is. Cute is a shortening of it that showed up in the early eighteenth century, and it just meant clever. A century later, it started to mean pretty for some reason (I guess clever is pretty?).
Acute showed up several centuries earlier in the late fourteenth century. Have you ever noticed that in medicine, a disease can be referred to as “acute”? Well, that was its original meaning, an illness that comes and goes quickly. It was the opposite of a chronic disease. It moved into general usage as a word for sharp or irritating in the fifteenth century, and then intense in the eighteenth. Acute comes from the classical Latin (of course) acutus, which has meanings ranging from sharp and quick to keen and cunning. It’s the past participle of acuere, sharpen.
So how about the other words that end in -cute? Execute first showed up in the late fourteenth century, coming from the Old French executer, and before that the Medieval Latin executare and classical Latin execut-, a prefix meaning, well, execute (not in the capital punishment sense but in the do something sense). The -cute is really a coincidence as the Latin word for execute is exequi. The ex- is a prefix meaning out and the -equi comes from sequi-, follow. It should not surprise anyone to learn that that word is where we get sequel from. So, execute is follow out and the -cute suffix is a coincidence.
Persecute is a lot like execute. It showed up in the mid-fifteenth century basically meaning the same thing it does today. It comes from the Middle French persécuter, pursue or torment, and classical Latin persecutus, the past participle of persequi, pursuit. The per means through and again, the sequi part means follow, meaning persecute really means “follow through”.
When prosecute first showed up in the early fifteenthcentury, it meant follow up or pursue. It comes from the classical Latin prosecutus, the past participle of prosequi, continue or follow after. It didn’t start having to do with the law until the late sixteenth century, although it kind of makes sense since prosecuting is following someone with the law. Kind of. Loosely. The prefix pro- means forward, making this word “follow forward”.
Electrocute is funny. First of all, it’s a very recent word, showing up in the late nineteenth century when we started killing people with electricity. It’s just a mix of electro- and execute! Oh, and it’s one hundred percent American English made. We should be so proud.
TL;DR: Cute comes from acute. All other words with the suffix -cute come from the word for sequel.