lliana, I recently cut small (one eighth to one third inch) girdling roots from a sturdy five year old maple that we had transplanted two years ago. I used a claw and my finger to gently tease away the dirt to trace out the main lateral roots and see where the girdling originated. When I found that I used a Felco pruner and easily cut the small offending encircling roots. I kept the main roots wet as water transpiration will occur with even little exposure, then immediately replaced removed dirt and placed mulch a good 3 inches from the root flare and watered again. I was careful not to cut the root flair/tree itself.

It may appear you have roots only on one side as I did too. But interestingly, it took the gentle dissection to determine the maple had two lateral roots on the other side, with one of them being the origin of the girdling roots. GL.

I should add that the tree is in decline and struggling so this is a last resort. It did. It leaf out last year and this year we have die back and epicormic buds signaling distress. I ended up cutting the roots that were problematic this morning. Will cover it back up asap!

And here is my previous thread with the tree history http://forums.gardenweb.com/discussions/3753310/does-my-japanese-maple-need-pruning?n=4

Just wanted to update this!! After 3 years of the tree deteriorating, I cut the girdles roots last spring. My tree is back!!!! I'm so happy!!!! Just need to get someone to prune the die back but it's doing amazingly well considering!