Was Casper Smart Cheating On Jennifer Lopez With Transsexuals? -- No Way, José

Casper Smart did NOT cheat on Jennifer Lopez with two transsexuals -- and he's prepared to sue the website that claims he did ... so says Casper Smart.

As TMZ first reported, JLo and Smart split up a few months back ... and it had nothing to do with Smart's alleged sexcapades.

But Smart is pissed that TheDirty.com claimed he had flings with two transsexuals he met on Instagram ... so his lawyer has fired off a letter to the site's founder, Nik Richie, denying he's ever met, kissed or had sexual relations with either of the transsexuals in question.

Smart says he didn't send them dirty pics and flat out denies cheating on Jennifer.

Smart has given the site an ultimatum -- either retract the story or get sued.

Smart's lawyer also sent a threatening letter to one of the transsexuals who has been talking to the media ... imploring her to sign a declaration saying they never met Smart.

TMZ reached out to Richie for a response ... and here's the part we can post: "Casper, go get a real job. I heard Instagram is hiring over in their compliance department ... Stop blaming everyone else for your problems."