Though the song had been introduced (in embryonic form) on the tour to support 1975's, The Hissing of Summer Lawns, "Coyote" was a significant musical departure: where Hissing was ornate with pianos, layered vocals and percussion, "Coyote" was stripped down to electric and acoustic guitars and a fretless bass guitar played by legendary virtuoso Jaco Pastorius. In a sense, this was similar to Mitchell's early albums, but the sound was extremely spacious, even repetitive, with the verses made much longer and more like a long story. Thus, although this is one of the faster-tempo songs on Hejira, it still lasts for an even five minutes. (Most songs on Mitchell's earliest albums were fewer than three minutes.) Mitchell's guitar itself was in an unusual (low to high) C-G-D-F-C-E tuning - presumably a type of open tuning designed to play a seventh, ninth, or even eleventh chord.
Lyrically, "Coyote" is concerned with the difficulty of establishing any sort of connection with people who come from "different sets of circumstance" (as the song has it). In particular it describes an encounter (which turns into a one night stand) between the narrator (possibly meant to be Mitchell herself as there is a reference in the lyrics to her coming home from the studio) and "Coyote", a ranch worker. Coyote represents nature contrasted with the narrator's big city (presumably LA) life where "pills and powders" are necessary to "get them through this passion play". The aforementioned line is also a reference to Bob Dylan's Rolling Thunder Revue, which Mitchell was a part of in the fall of 1975.
A version of "Coyote" was performed by Mitchell with The Band for the concert movie The Last Waltz and is included on the soundtrack. The song was also covered by Spirit of the West on the 1992 Mitchell tribute album Back to the Garden.