Without in English means both "bereft of" and "outside of", and even if the latter sense has become archaic it still persists as a learned usage and is a reasonable translation here of Latin ex.
No, the sense of "ex" here is very definitely "bereft of", and it is specific to financial English. (Why do you think it's being contrasted with cum?) Buying ex-dividend means you don't get the dividend.
It develops, through the phrase "ex-dividend date", from a special sense of ex in Latin when applied to times, meaning "after". (You can see exactly the same thing happening in English phrases like "from now on".) Originally, ex-dividend date referred to a date after the dividend date. This was reanalyzed as referring to a date upon which the instrument becomes "ex-dividend" [nonsensical in Latin], which required a reanalysis of ex as pertaining to the dividend rather than the date.
It is an error to talk about translating "Latin ex" here; this isn't a Latin ex.
