The equivalent of "side of beef" seems to be carne en canal, or in shortened form, canal (female), but I'm not sure if this refers to the actual piece of the animal or to the mode of cutting. In Argentina, Uruguay, Paraguay and very possibly other countries in South America, the name for this in common parlance and in the industry is media res, i.e. literally "half a cow".
Res is a specialized word, used practically only in the context of livestock farming and processing; it's a general term for farm animals. (Not to be confused with the Latin expression in medias res.)