I want to tell a story and in a part I want to say:
He saved his owner's life.
I'm not sure if this sentence is correct:
Er hat dem Besitzer das Leben gerettet.
Yes, "to save sb's life" is translated as "jdm. das Leben retten" and, hence, your German sentence is correct.
Except for two minor mistakes. Note that his is translated as seinem, while dem is the translation of the article the.
Also, it is gerettet at the end of the sentence. I guess this was just a typo, wasn't it?