Yes, the backup is stored on your own server. You can choose to have the backup active (recommended) or not: you can find the setting on Settings > ShortPixel > General.
However, as long as you keep the backup on your server, it will also consume more disk space. If you notice that the backup folder uses too much disk space on your hosting account you can choose to remove it. We recommend making a copy – via FTP for example – of the backup folder so you can restore the images in the future by uploading the backup folder back to your server.