The fan can usually be removed from the heatsink separately.
The heatsink will be clamped to the mobo in one of several different ways.
If you’re reomoving the HeatSinkFan (HSF) as a unit be advised that the thermal paste between the HSF and processor can act like glue.
Processors have been ripped out of their sockets by folks not knowing what they were doing. This is bad.
I use a very slight twisting/lifting motion to release the HSF.
There have been times where I had to use a hair dryer to warm the HS which in turn warms/loosens the thermal paste