Yeah, but maybe Looking Glass has batteries or something. Though severing the cable does make alot more sense.
While the cable may also be a power supply, I took it more as the connection to the radio tower that emmits the jamming signal since you cant jam a radio signal from underwater. The whole reason for them to go to the Looking Glass was to flip a switch that would stop the jamming so it just seemed really silly to me that they would choose to try to swim to a flooded chamber, which would kill Charlie, instead of just axeing the cable.