The actor, who has starred in shows such as Jericho and The Event, sparked outrage from Twilight fans when he began tweeting about Kristen Stewart's infidelity to Pattinson.
"Just saw Pattinson on #DailyShow trying to figure out what took k-stew so long to look around with this douche astride her," he wrote, adding the hashtag: "#holytwit."
However, he soon received angry messages from Twilight fans and added: "Hey #twilight geniuses--try decaf! A little too worked up over a skinny vampire."
Sweeney went on to retweet several messages he received criticising him for his tweets but continued to add messages, saying: "Nice language twi-hards. Or should i say tards? Love the inchoate indignation [sic]."
He added: "Dear twihards. Its been a difficult time. First tom and kate. Now rob and kristin im in a spiral. Youre caring abuse has been a comfort [sic]."
Pattinson has recently been promoting his movie Cosmopolis, though he has remained tight-lipped about his relationship with Stewart, instead choosing to discuss the role of the media.
Both Stewart and Pattinson have reportedly chosen not to attend a number of upcoming Twilight conventions, while Stewart has allegedly cancelled her appearance at the MTV VMAs to avoid presenting an award with Pattinson.
Robert Pattinson and Kristen Stewart in pictures: