Yes, you can find a replacement dongle on our accessory page and easily re-pair the new dongle to your mouse. In the meantime, you can always continue using your mouse in Bluetooth mode.
This link will take you to the replacement dongle for the original Rival 3 Wireless. It will not work with the Rival 3 Wireless Gen 2.
You will need to download SteelSeries GG to pair your replacement dongle.