The album charted at number 4 in the UK and number 66 in the US, but received a mixed response from critics. The singles lifted from the album were "Dagenham Dave" (which reached number 26 in the UK Singles Chart in August 1995) and "The Boy Racer" (which reached number 36 in December).
The nature of the album is different from past Morrissey releases, such as the inclusion of two tracks which surpass the ten-minute mark, the near two-and-a-half-minute drum solo courtesy of Spencer Cobrin which opens the track "The Operation" and the sampling of a Shostakovich1 symphony. AllMusic described it as " art rock album, complete with strings, drum solos and two ten-minute songs."
According to Morrissey himself, the title refers to "the school of hard knocks"; that is, boxing (a southpaw being slang for a boxing left-hander and grammar a reference to British grammar schools). Another reference to boxing is the original cover photo, a photo of boxer Kenny Lane taken from the April 1963 issue of boxing magazine The Ring.
Spin magazine described the album's musical style as " from the crushed flowers studio formalisations of last year's Vauxhall and I, building instead on the earlier Your Arsenal, Morrissey's sly, unexpected blending of rockabilly and glam."
Southpaw Grammar was released on 28 August 1995 by record labels RCA in the UK and Reprise in the US. The album charted at number 4 in the UK and number 66 in the US. On its release Southpaw Grammar was an eyebrow-raiser for fans and critics alike.