It uses batteries whenever there is a cord plugged into the input (guitar) side, even if the effect is bypassed (clean mode). So, if you want save batteries, make sure that you unplug your guitar from it when you’re done playing. Almost all guitar effects pedals work the same way.
Don’t worry about it using power when it’s bypassed though, the Big Muff uses only a very small amount of power to get it’s effect. The battery should last a very long time as long as you remember to unplug the guitar when you’re not playing. 