Marcus Leyshon was due to contest the Horbury and South Ossett seat on Wakefield Council which is currently held by Labour, at the polls in May.
In separate posts on a Twitter account in 2014, Mr Leyshon used a racial slur to describe Asian people and an offensive term in relation to gay people.
Asked for comment about the posts, a Conservative spokesman said: "Mr Leyshon has been suspended pending an investigation."
Party sources said he stood down as a candidate after he was suspended and he has been replaced by another Tory member who will contest the seat.
Mr Leyshon has been contacted for comment but not responded.
Conservative Party literature seen by the Local Democracy Reporting Service said he'd decided to stand in the ward after flooding hit his native Horbury Bridge area last year.
Nominations for candidates at the local elections opened on Thursday and close on April 8.
Local Democracy Reporting Service