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AxisCut selection Mode :
This mode allow to select points / polygons that are left or right on any axis

Starting Shape
Here, only points that are >=0 on X axis will be selected
You can ignore point equal to 0 by checking the corresponding option
Result : only point with strictly X > 0 are selected
You can do selections on multiple axis at the same time.
Here an example with polygons, all on X+,Y+, Z+
Result... not very clear
Here I've set a new surface to selected polygons, so you can clearly see that some are not selected, it's because they are on -X,-Y,-Z
You can use the Revert option to do the opposite
you can also force to not select polygon having a point at 0 on axis
If you geometry is not well placed, you can fix it
Use the Lock vertices near 0 function
and Set the max distance from 0 value
NB : the update button will find automatically a good value for your geometry.