Yes, cutting a tree's roots can cause it to fall, particularly if major support roots are severed. In extreme cases, trimming roots can affect the tree's structure and stability. Many crucial roots are located just below the soil's surface. If you make severe cuts to roots more than 2 inches in diameter, you risk impacting the tree's water flow and its ability to withstand severe winds or storms. Even cutting roots less than half an inch in diameter under or outside the tree's canopy can cut off its water supply, causing it to decline, die, and eventually topple.

Unfortunately, palm tree stumps are one of the most difficult types to remove due to how their roots grow. Unlike other trees, palm tree roots grow horizontally and vertically. Palm tree roots grow as deep as three feet into the ground, although soil and growing conditions could mean they go as far as 50 inches into the earth. 

If you want to be able to repurpose the grass in the area where you removed a stump later, you’ll have to dig quite deep—and perhaps wide—to trim away all the roots.

You should avoid cutting off the top of mature cherry trees. This process is called tree topping, and it’s not recommended for cherry trees—or any trees, for that matter. Tree topping removes between one-third to half of the length of the tree trunk, resulting in structurally unsound, fruitless suckers. The only exception is for saplings. Young pie, sour, and tart cherry trees that are over 30 inches tall in the fall or winter before the tree blooms can benefit from heading cuts.

Yes, you can prune a palm tree with a chainsaw, but a chainsaw is overkill for a job like this. You risk damaging the tree if you make a bad cut. More commonly, you’ll need pruning shears or a serrated knife to trim a palm tree, or you can use a specialized pruning saw instead of a chainsaw.