口 is the indexing mouth radical, marking
嚎 as a vocal-emission verb — here, the long howl of grief or a wolf's drawn-out cry (
嚎啕大哭,
狼嚎). Sibling mouth-radical chars
哭 (weep),
嚷 (shout),
嗥 (yelp),
喊 (yell) all share the mouth-on-the-left + sound-mimicking-phonetic pattern.