Green’s Dictionary of Slang

1. (US, Western) very big or powerful, hard to overcome.

1829		Western Monthly Rev. III 129: They were in the habit of managing a wild, or as the phrase was, a ‘severe’ colt [DA].
1889		Harper’s Mag. Jan. 270/1: He never killed a man who did not deserve killing. [...] He is called in the language of the country, a ‘severe’ man [DA].
1907		S.E. White Arizona Nights 5: ‘Trailer,’ said he sadly, ‘is a little severe’ [DA].

2. excellent, first-rate.

1982

Eble Campus Sl. Fall 4: severe – good, great, excellent.