The manga adaptation of Mewtwo Strikes Back! has only ever been published in the July 1998 issue of CoroCoro. It has never seen release in a collected volume anywhere in the world.
Differences between the anime and the manga
In an interview with Animerica magazine, Toshihiro Ono states that he was instructed to include Mewtwo's origin story in the manga adaptation. Since Ono only had the movie's script to work with (the original theatrical version of the movie was released approximately two months after he had begun work on the manga) and the radio drama The Birth of Mewtwo had not been created yet, Ono created his own original explanation of Mewtwo's origin.
Mewtwo and Dr. Fuji have a closer relationship than they do in the film, with Mewtwo considering Fuji like a father.
Mewtwo physically talks, using its mouth, instead of through telepathy.
Dr. Fuji's motivations are different than in the movie. In the manga, he is motivated to clone Mew out of a desire for revenge against an institute he was expelled from.
Dr. Fuji meets Mew face-to-face and befriends it, leading to his acquiring one of its eyelashes. It later leaves him when he becomes consumed by his work.
Giovanni's ultimate plan is to have Dr. Fuji mass produce Mewtwo and create an army of mindless living weapons. Fuji begs Mewtwo to destroy the laboratory to prevent this and it does so, causing Fuji's death.
Instead of sending out invitations to trainers it selected, Mewtwo appears at a tournament called the "CoroCoro Cup" and challenges its winner to a battle. After defeating him, it challenges the trainers in attendance to visit it on New Island in a week's time.