If I cut off the water for a limited amount of time, should I also cut off the power to the tank?

What is "limited "? Hours, days or more? If hours, do nothing. If weeks or longer, set temp to vacation or very low.

With an electric unit it is easy to just turn the breaker off.

With gas follow Brians advice.

Chuck

Not necessarily. You don't need to cut the power connection to your water tank to switch off the water connection.

Like Ma0641 queried, how long is "limited amount of time"?