There is a simple solution to removing roots that are uplifting your walkway or patio pavers, but it isn't always an easy job to execute. Roots from trees or even shrubs can grow large enough and near enough to the surface to dislodge pavers made from most any material, making the paver surface uneven. In addition to marring the aesthetics, it also creates a tripping hazard. When it comes to invasive roots, the problem will not get better with time and should be corrected at the earliest opportunity before more damage is done.
Remove all of the pavers affected by the roots plus enough rows so that you have good access to the soil surrounding the problem roots. Use your gloved hands, a spade or pry bar to lever the pavers off of their base.
Number the pavers with chalk if needed so that you can replace them in a particular pattern. Set the pavers aside where they will be safe from damage.
Excavate around the roots, removing the substrate under the pavers and the soil surrounding the roots. Remove enough soil so that you expose and can clearly see the sections of root you want to remove.
Sever the unwanted roots cleanly with a sharp cutting tool. A spade will cut through small roots less than 1/2-inch, loppers work for roots up to 3/4-inch thick and a small axe will work best on roots that are larger in diameter.
Pull all of the root pieces out of the soil and discard them. Make sure the remaining roots all fall below the surrounding surface of the soil.
Back fill the excavated area with the topsoil removed earlier to bring the area level with the surrounding soil.
Cover the soil with a layer of the substrate used to set the pavers, usually gravel or sand, leveling it out to a smooth surface.
Replace the pavers into the desired position tamping them down with the wooden handle of your spade or a rubber mallet to set them.
Brush or wash off any chalk marks on the pavers and fill in between the pavers with remaining sand or aggregate, if applicable to your installation.