No, you cannot turn off your WHOOP Strap because it remains powered on as long as it's still charged.
NOTE: The Strap will enter a low-power mode to conserve battery life if it's off the wrist and remains motionless.
How do I know if my Strap is in low-power mode?
You'll know your Strap is in low-power mode when the green light emitting diode (LED) on the bottom (of the Strap) turns off.
NOTE: The Strap does not collect data when the green LED on the bottom of the sensor is off.