Your injured mouse will have endured a slow and painful death.
If you can see a few mice, then there are a whole lot more that you can’t see. If there is plentiful food for mice, it is quite likely that rats will also find it sooner or later.
There’s nothing cute and friendly about mice, they carry some horrible diseases and can cause extensive damage. You don’t want the little blighters gnawing through electric cables.
Get some decent quality rodenticide or if you don’t want decomposing mice under your floorboards, get some strong snap traps, baited with peanut butter. I’ve been battling a family of mice living in the walls of the farm office for a few months. I can’t poison them because of the dogs, so trap them. Catch about 4 or 5 a week.
Failing that, try this method…
Anybody feed the birds? - Page 2 - Cardiff City Forum - https://cardiffcityforum.com/threads/anybody-feed-the-birds.17310/page-2#post-643899