well i guess you can leave a stump with possible fungus problems that are not good or dig it up . i would dig it up.it doesnt have to be as messy as it mite seam though it will take a little while.you just take the turf of with a sharp spade a bit like when you buy turf so you leave some soil on the roots.i would put some polythene all over the grass your not moving .hard to say how big the root ball is without knowing how big the acer was realy .you could use ply wood to i guess.carefully put the cut turf to one side.then dig you stump out and shake as much of the soil back in as you can.make up to level with a little more topsoil and tread it down well till it is level with the rest.rake it lightly and tread it down again if need be .then carefully put your turf back wear it was.water that area realy well after youve moved the wood/polythene.any little bits of dirt on top of the grass just gently rake over.in a couple of weeks you will hardley notice . try not to walk on the turf you moved to much for a good while either.it wont take that long i doubt as acers even big shrubs arnt that big .

There are two ways to get the stump out and they both leave a mess: dig it out, or burn it out by starting a bonfire over the top. The latter is easiest but you need to be really careful if there is a chance that you have a lot of organic material in the ground (like peat) as this can start an underground fire. I agree - dont leave the stump in.

thank you for your advice looks like we are digging it out. We are very sad for the loss of the acer as it was a beautiful tree, we do still have two in the back garden though.

yes i bet you are but wear there was death you can have new life so dont worry.take care all my advice good or bad is free lol your more than welcome.