Domitor (without the -um, which is unnecessary here) would be a breaker in the sense of a breaker of wild horses. It doesn't have to do with physical breaking, which is what you want.
Instead, you can use a derivative of a verb such as frangere – e.g., fractor. Though this word is unattested (at least in classical Latin), it's easy enough to derive it. You probably also want a plural form of 'idol.' Though the word idolon is used mainly of apparitions or ghosts in classical Latin, not physical representations of persons or deities, I'm fairly certain it can have the required meaning in ecclesiastical Latin. So you could say either idolon fractor (using a retained Greek genitive plural ending) or idolorum fractor (using a Latin genitive plural ending).
Alternatively, you can use some single-word compound modeled on saxifragus ('rock breaking'), such as idolifragus.
The plural of idolon/idolorum fractor is idolon/idolorum fractores, and the plural of idolifragus is, for a group of men or a mixed group of men and women, idolifragi; for a group of women, idolifragae.
Updating to add that if you want the term to apply to images in a more general sense, not specifically to religious idols, the Latin noun imago can work: imaginum fractor or the quite ugly imaginifragus.