There are several synonyms that can be used in place of the phrase "mad as hell". One option is "furious". This word denotes extreme anger and frustration. Another possible synonym is "livid", which signifies a deep and intense anger that is often associated with rage. "Irate" is yet another alternative, which can convey a sense of indignation and offense. One more synonym that can be used in place of "mad as hell" is "enraged", which implies a state of anger that is beyond control. All of these words can be used effectively to convey the emotions of extreme anger and frustration.