I don't know how you can "train" a cat to be a mouser. I thought it just came naturally. When Tubby was staying with my mom, there were quite a few entertaining mouse sessions. My mom lives with a woods on two sides of her house, and an old, old barn and fields on the other two sides, so it's no wonder she gets mice in the house. Tubby loved it. He would know when a mouse was around. He would sit and look at the cabinet door under the sink. When he did this, my mom would know there was a mouse around.
In this picture you can see that my mom has set a mouse trap out, but has also opened the door so Tubby could get at it if it emerged and made it past the trap.
In this picture, the mouse has gotten past all traps, except the big black one looming nearby.
Tubby would play with them until they were exhausted, but my mom would usually take it away from him before it was dead. She was worried he would push it to exhaustion and it would climb in the pipes and die and then start smelling. I could usually not watch because I felt sorry for the poor mouse. I know it's nature and all that, but Tubby would normally just play with it and the poor mouse was probably scared to death. Tubby had fun though. 
I have many more mouse stories to tell, but it's late.....
Tubby
Spring 1986 - Dec. 11, 2004
RIP Big Boy
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Peanut
Fall 1988 - Jan. 24, 2007
RIP Snotty Girl
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Robin
Fall 1997 - Oct. 6, 2012
RIP Sweet Monkeyhead Girl
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