Evicting mice without hurting them

I have nothing against mice, I like them, in fact if I didn't have neighbours I'd probably leave food out for them. Today, for just the slightest instance, I think I saw one running along the bottom of the fence. I know my next door neighbour have had trouble with them before so that's probably where it came from but has probably emigrated to my garden.
Below is a quick MS Paint drawing of my garden to better explain my forthcoming plans. (I have a friend who is an artist and I don't think even she could have drawn it with such wondrous detail as I.)

I added the irrelevant so that I could possibly use it again if necessary and maybe explain scale. Now, at the back of my garden, 4, is where I saw the mouse. I'm guessing that if the mouse was living anywhere it would be in a warm heap of vegetation. I did build a cage around the heap using old wood but the heap got too big and, possibly with help from my dog, it burst and so I abandoned it altogether. Because of the overhanging ivy, the compost and wood I couldn't be bothered to collect and my dog's obsession with the female dog in the garden behind, I decided to build my border a few feet from the fence leaving a gap.

I am going some where with this... As I have left over mud with no purpose except for me to play with and build a border akin to a fortress wall, I was just going to pile the excess onto the area I'm not using (4) and then the mouse couldn't sleep there any more, job done.. but that might bury the mice and I don't want that, no no.

So should I:

A: Pile the mud on, the mice will escape through the thick compost long before it is heavy enough to crush them.
B: Clear the whole area of anything I don't need there and make sure to tuck my trousers into my boots that day!
C: Use your big idea which you'll need to tell me in your reply.

Fingers on buttons.

 

What sort of mouse was it?

If it's a common house mouse it's much more likely to be living in a shed, garage, or your house!

 

I just leave mice to get on with it.
See them fairly often, but the local cats keep them under control.

I had one set up home in my greenhouse one year and had to poison it, but if they are outside I just dont bother about them, its only wildlife afterall.

 

Is the mouse doing any harm. If the answer is no then I would just leave it alone.
If you get the chance to watch them in close up they are quite charming.