For iOS:

Yes, you can play your saved game on multiple iOS devices by signing into GameCenter. When you sign into your GameCenter account, Space Miner Wars will automatically link your game account to your GameCenter ID and you will be able to access it from any device that can access GameCenter. However, while you can access your account from multiple devices, you may only play on one device at a time. If you purchase a new device and still want to play your saved profile on it, please make sure that you sign into GameCenter to save your profile before getting rid of your old device. 

For Android: 

Currently we do not have a feature that allows accounts to be played on multiple Android device nor play accounts cross platforms. Your saved profile is attached to your device. Unfortunately, we are not able to bring your saved profile over to your new device.