Sure, what's the issue? The Arris SB6141 is a wired modem, only a modem.
You keep the modem from TWC that has the telephone device, but the internet modem part of it is disabled by TWC. Since the internet part is not usable you no longer have to pay the rental fee, even though you still have the modem. Yeah, it makes no sense.
Now, since your modem you received, and rented, from TWC no longer works for internet, you hook up your Arris SB6141 for internet access.
You will need a router if you have more than one device to access the internet.
A connection kit is available from TWC that contains all you need to hook up your new modem, and keep your old modem for the phone access.
Post a question and we'll try to explain if this is still unclear.