When you see a tree getting cut down, the first thing to do is talk to the person removing the tree and find out why they are removing it. Sometimes trees are damaged or diseased, so they legitimately need to be cut down. In other cases they get cut down simply for aesthetic reasons.
Do research to find out if the tree is being cut down legally. Some species are protected even if they're on private property. If you're concerned that the tree should be preserved, it's time to take action.