Yes it is the downside but never punish her cos she is just doing what comes natuarally to cats.
Mine went through every mouse in the garden last year and one of them I saved, it ate cheese in a box once it had recovered from the shock and I took it to the bottom of the garden, 100ft, and put it in some long grass thinking it would be safe.
I turned my back and Misa and Sasa were hunting it, they went staright to the place I had hidden it and the idiot mouse didnt stay put but ran out and it was goodnight mousey. I was so upset.