How do format time machine to erase all the files to start like a brand new one?

First, head into System Preferences > Time Machine. Click Select Disk, then select your Time Capsule and click Remove Disk. This will stop the current backup schedule.

Next, use AirPort Utility to erase the Time Capsule.

Finally, return to System Preferences > Time Machine, click Select Disk, and follow the steps to begin backing up to your freshly-erased Time Capsule.

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• If you are using Mac OS Monterey you can open system Preferences - open the System Preferences Menu and you can erase from there.
• If you are running Mac OS Big Sur or earlier then please restart in the Recovery Partition (hold down Command + R on startup) and using Disk Utility erase the internal drive. Then exit Disk Utility and install Mac OS on your internal drive.

Are you using an Apple Time Capsule device, or a regular USB hard drive?