Lennie likes to pet small, soft, furry things. He always kills the mice, according to George and by his own admission, but evidently he doesn't mind their being dead, at least for a while, as long as he still has a small, soft, furry thing to pet.
In Chapter 1, George says:
"Your Aunt Clara give you a rubber mouse and you wouldn't have nothing to do with it."
"It wasn't no good to pet."
A rubber mouse is small but it isn't soft or furry.
Lennie may not be as simple as he seems. As big and strong as he is, he ought to have learned how to handle mice so as not to kill them with his petting. It seems possible that he has a dangerous side to his nature and that he actually kills the mice deliberately. He might enjoy the killing as much as he enjoys the petting. And this might tend to explain why he hangs on to dead mice. He explains to George:
"I'd pet 'em, and pretty soon they bit my fingers and I pinched their heads a little and then they were dead--because they was so little."
This sounds a bit different from killing them with kindness. Rather than killing the mice with too much petting, Lennie kills them when they bite his fingers. He may have a lot of pent-up anger in his system which he takes care to hide, even from his friend George. When he kills Curley's wife in the barn, it seems like a pretty violent act and not an accident caused by a man who doesn't know his own strength. Before killing Curley's wife, he has just finished killing the puppy he was given by Slim. All this killing makes Lennie seem somewhat sinister. Even if he is like a big child, there are some children who are gentle and some who are sadistic.