Let's say that you want to cut an object into 4 pieces, create the 4 objects that are supposed to cut the object, stick the 4 objects to each others with the Snap option for example:
Duplicate the object and one of the 4 cutting object, give to the object a Boolean modifier in Intersect mode, apply, then duplicate again the original object and another one of the 4 cutting objects:
For the example you show me, create a plane, subidivide it, sculpt it a bit, put it where you want the cut to happen:
Duplicate the objects, use the Boolean modifier with the Difference mode to get the first half of the object:
Duplicate the original objects again, select the plane, in Edit mode select all and invert its normals (AltN > Flip), you get the other half:
