"The offensive attitudes and statements discovered on James' Twitter feed are indefensible and inconsistent with our studio's values, and we have severed our business relationship with him," Mr Horn said.
Mr Gunn said in a statement that he took full responsibility for the tweets.
In a series of tweets posted on Thursday, Mr Gunn addressed the controversy surrounding his old posts.
"I viewed myself as a provocateur, making movies and telling jokes that were outrageous and taboo," he wrote.
"As I have discussed publicly many times, as I’ve developed as a person, so has my work and my humor."
Mr Gunn wrote and directed both of the first two Guardians of the Galaxy films, which starred the likes of Chris Pratt, Zoe Saldana and Bradley Cooper.
The two installments of the franchise brought in more than $US1.5 billion at the global box office.
A third installment in the series was due to be released in 2020. It is not clear who would now direct the films.
Mr Gunn has been an outspoken critic of United States President Donald Trump and said in December that he did not care if his stance resulted in him losing fans.