There are two reasons for this in the book. First, there is the question of hygiene. Mice are dirty and they carry germs. This is the implication, because George never allowed Lennie to keep a dead mouse, no matter how much Lennie wanted to pet it. George makes Lennie throw away these dead mice.
Lennie’s closed hand slowly obeyed. George took the mouse and threw it across the pool to the other side, among the brush. “What you want of a dead mouse, anyways?”
The second reason comes from the fact that Lennie does not know his own strength. According to the book, Lennie is extremely strong, but he is slow intellectually. So, he always winds up killing them.
“The hell with the rabbits. An’ you ain’t to be trusted with no live mice. Your Aunt Clara give you a rubber mouse and you wouldn’t have nothing to do with it.”