Sure. It happens routinely in physiology. Most ions are composed of multiple atoms—that is, they are charged molecules. So any chemical reaction that splits one of these molecules has split an ion. Split ATP into ADP and Pi, and you have split an ion.

Attested since about 1567, from Middle Dutch splitten (“to split”) and/or Middle Low German splitten (“to split”), both ultimately from Proto-West Germanic *splittjan, an intensive form of Proto-West Germanic *splītan (“to split”), from Proto-Germanic *splītaną (whence Danish splitte, Low German splieten, German spleißen), from Proto-Indo-European *(s)pley- (“to split, splice”).

Compare Old English speld (“splinter”), Old High German spaltan (“to split”), Old Irish sliss (“splinter”), Lithuanian spaliai (“flax sheaves”), Czech půl (“half”), Old Church Slavonic рас-плитати (ras-plitati, “to cleave, split”).