The Liverpudlian provoked his rival ahead of their all-British middleweight grudge match on Saturday night at the Manchester Arena.
The former world champion confronted Eubank Jr about his private life and urged his rival to come out.
But Eubank Jr appeared to laugh off Smith’s attempts to unsettle him, stating: “my private life is my private life”.
He then made a personal insult of his own concerning his rival’s relationship with his wife before adding: “If you would like to ask me a question just slide into my DMs.”
Sky Sports presenter Anna Woolhouse would later intervene to make an apology on behalf of the broadcaster.
She said: “We would like to apologise if you have been offended by the offensive language, personal and homophobic remarks made up on stage.”
The bout, which materialised in the aftermath of Eubank Jr’s cancelled fight with Conor Benn, following his failed drugs tests, has endured a bitter build-up.
Eubank Jr and Smith have previously shared the ring during sparring sessions, with regular taunts concerning their exchanges and who came out on top.
Smith is adamant, despite moving up to 160 lbs, that size difference will not be a deciding factor in the fight.
“Don’t be fooled, thinking Chris Eubank is going to walk all over me because it’s at 160,” said the Merseyside fighter. “If you want to shoot your shots early doors, make sure you don’t miss, mate. If he comes to me to make a fight, he knows I meet fire with fire.
“And that’s if he’s got the legs to do that for 12 rounds at 160. He’s going to have to go some to budge me – not many people have. Canelo [Alvarez] done me with a body shot; he was the best fighter in the world.
“Nobody else has come close and Chris Eubank Jr. is not going to come close either. If he comes for me early doors, he’s in for a long night.
“If he tries to outbox me, good luck to you. Hopefully, your size works in your favour because I don’t think you have the fundamentals to box me like that.”