There likely isn't an option in the game itself, but you can probably disable them from your device.
On Android 4.1 and newer, you can open Settings, then Apps, then Tapped Out, and then uncheck the "Show notifications" option. If your Android version is older than that, you could use Greenify to stop apps from running in the background, which should stop Push Notifications, although it may have side effects if the game requires running in the background.
For iOS, you can see this question on Ask Different, but basically you go to the app's settings, then Notifications, and then turn them off.
