Siegebreaker keeps everything on your phone, in storage only the game can read: your campaigns in up to three slots, a Daily Siege in progress, your career records and the summaries of the runs you have finished, and your settings. We never receive any of it, so we can't recover it for you.
If backup is turned on for your phone, Android may include the game's data in the backup Google keeps for your Google account, and restore it when you set up a new phone or reinstall the game. That backup is Google's, under your own account's settings: you can check it in your phone's Settings, under Google and Backup (the names vary a little between phones).
Without such a backup, uninstalling Siegebreaker deletes your campaigns and records for good.
The full game itself is safe either way: it belongs to your Google account. See Getting the full game on a new phone.