How to disconnect a component with a microcontroller output?
Changing the common voltage [GND in this case], can cause errors in interfaces.  We can put in a MOSFET to switch the power supply of the chip in this case, instead of switching the ground.

Use a P-type MOSFET to connect between the 3.3V rail and the 3.3V input of the Open Log.  An example is the BS250.  The Gate of the P-type MOSFET should have a 100K pull up resistor to 3.3V, so that the voltage of the rail "stops" the MOSFET from turning on.  Source should be connected to 3.3V, Drain is connected to the Open Log.  If you want to turn the OpenLog "ON", have the uController pin that is connected to the Gate of the MOSFET be pulled LOW.