An informal definition of "blast" is a severe verbal reprimand, and it is unlikely you've never heard it used that way because it originates in the US in the late 19th century. "Put on blast" means to embarrass publicly by admonishing, and also originates in the US, but is much more recent. Compare to "put on full blast," (sound familiar?) which has a different but related meaning, but like all these uses originate from Old English blæst "a blowing, a breeze, puff of wind," and later, blast furnace, the idea of forcing air to increase combustion for smelting iron.