Hidden within your straightforward question are a couple of items that should be addressed.
1. I would certainly use such compost - and do - in my home garden. Having said that, there is always the fear for hanta virus and similar human disease issues. It's always important to avoid hand-to-face contact when handling any type of soil amendments. I would recommend wearing gloves, and avoid inhaling any particulate matter that could arise from the compost.
2. You have mice in your compost because (educated guessing) you are adding food waste to the compost pile but it's not getting hot enough to drive off the rodents. Any time food waste is added to a compost pile, it's important that the following be done:

• Never have food waste in direct contact with the soil.
• Never have it as the top layer.
• Always turn your compost pile and incorporate food waste at the rate of 1-3 quarts every 4-6 inches in compost depth. (Assuming this is the standard 0.6 cubic yard backyard composting bin.)
  
• Discourage rodents from burrowing into the compost pile from below by placing a piece of hardware cloth (1/2" mesh or smaller) under the composter. The cloth should be large enough to extend beyond the edges of the composter on all sides.
• Encourage a hotter compost pile by adding nitrogen (alfalfa pellets from the feed store are a nice way to do this - but you have to store the unused pellets out of the reach of mice . . .) and by ensuring that your compost has enough moisture. If you squeeze a handful of compost REALLY hard, while wearing a rubber glove, you should at least see a sheen on the glove. If you get more than 1-3 drops of liquid water from squeezing, it could be a bit too wet. That's pretty uncommon in home composting.

3. Getting the mice out of your compost: If you will empty the composter a fork-full at at time into a wheelbarrow (to apply to your garden plot) the mice will be alarmed and move away at least temporarily. Follow the directions in point #2 to avoid a reinfestation. In your situation I would wear knee-high boots to do the work - reduces the ick factor. :)

If you wish, send me your email address and I'll try to share information about a small rodent trap for use outdoors. It does kill the mice, in case that's a concern for you.