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:

[![enter image description here][1]][1]

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:

[![enter image description here][2]][2]


  [1]: https://i.sstatic.net/tuaHO.jpg
  [2]: https://i.sstatic.net/ewnKv.jpg