Mailboxes are either mounted on an outside wall, or affixed to a post in the ground. Posts are either planted in the ground, or bolted to a small concrete pad. The mailbox on a post can be removed for replacement, or the entire ensemble can be dug out of the ground. Either way, there are very few parts involved, so it's very easy to remove a mailbox.
How to remove a mailbox
Take a box off the post. If you do not intend to put a new mailbox on an existing post you may skip this step. If you are replacing a box, it must be the same type of mailbox, or it won't fit the post mounts. The mailbox may be attached in a number of ways. All of them involve nuts and bolts that are easy enough to find. Standard boxes are held onto a mounting plate at the top of the pole with at least four machine screws. These screws are at the bottom of each side with the nuts on the inside. Hold the nuts with a fitting wrench or pliers, as you loosen the screws with a screwdriver.
Take a box off the wall. Wall mounted boxes are held on by screws. Most units hide these screws inside the mailbox. You'll have to open the flap to find them. Removal is as simple or difficult as taking the screws out. Then depending on how long the box has been there, the wall behind it may be a different color.
Remove a buried post from the ground. Standard size mailbox posts come with a concrete filled cup at the bottom that looks like a rectangular planter. They're usually buried about a foot and a half deep. Use a shovel to dig around the post in a six inch radius. Dig deep enough to loosen the post. Then pull it out of the ground and fill the hole.
Remove a pedestal mounted post. The bottom pedestal stand will be bolted to the concrete pad with at least four bolts. Loosen all of them before completely removing any. If possible, have someone hold the post while you take the bolts out. If not, keep one hand on the post to prevent it from falling on you as you unbolt its support. Remove the concrete pad, if you wish, by digging around it with a shovel. Most of these are buried relatively shallow. Fill the resulting hole.
Fill the hole. After you remove a mailbox post or concrete base; put a plant in its place, or cover the spot with sod. First shovel all the available the loose dirt back into the hole. Find extra fill dirt in a ditch or use mulch if needed.