How to split/cut a polygon through OpenLayers split method and same editing save to the PostGIS?
OpenLayer's Split control is straight forward. You pass it a layer in the contructor and the control will split it.
If your layer has ONE feature and you split it using the control you will end up with TWO features in the layer.
Once youre ready to save to PostGIS, you can write those features to a number of different formats WKT, KML, GML, etc. And pass that to your backend webservice wether it be a GeoServer WFS-T or a PHP, C# or other back-end handler/service that will save the features to your postGIS database.
you can split or cut your polygon at server side by means of postgis function. in postgis ST_Split function makes what you want. this function is opposite of ST_Union...
following example has taken from postgis api doc. :
and another solution for this is that you can check JTS Topology Suite. it has lots of feature with Geometry Operations.
some example of operation: