I read this story as a kid in a collection of best science diction short story. It's told I think from the point of view of the clone. I think the reason for trying to redo his own life was so that a romance with his childhood sweetheart would have worked out better.
The Fifth Head of Cerberus, Gene Wolfe, 1972.
Probably the original novella, not the more extended novel that followed.
Somewhat similar. It's a woman instead of a man.
The Lives and Loves of Tiarella Rosa - in the short story collection "A Second chance at Eden" by Peter F Hamilton. (1998)
Full story here: http://www.e-reading-lib.org/chapter.php/72415/13/Hamilton_07_A_Second_Chance_at_Eden.html
After her husband dies, Tiarella has him and herself cloned. She ensures that the two children's lives are as close to her own life as possible so that they will fall in love when they meet.
There's an interesting alternative to this in the C. J. Cherryh book Cyteen where the state clones an assassinated leader and arranges her life so that it mirrors that of the original in the hope that the new clone turns out with the same mental outlook and capability as the original.
Lots of political machinations in it as well as the view of life from the clone's view.
While this isn't a close match, I am reminded of this William Tenn story:
His second story, the widely reprinted "Child's Play" (1947), told of a lawyer who creates people with his Build-A-Man kit, a Christmas gift intended for a child of the future. After publication in Astounding Science Fiction (May 1946), Tenn was soon hailed as the science fiction field's reigning humorist, and during the early 1950s, readers of Galaxy Science Fiction looked forward to issues featuring his satirical science fiction.
A guy who is losing his girlfriend to a pushy rival gets delivered a "Build-A-Man' kit from the future. He decides to build a new girlfriend clone with it. He first practices a couple times - once making a baby but he forgot the belly button.
Finally ready, he decides on one more practice run and duplicates himself. The copy destroys the disassembler unit and the two are arguing. The clone thinks the guy is a wimp for not going for the girl himself. At this point the cops from the future show up and have to decide who is better, the man or the clone, and they disassemble the original man.