If i got the question right, yes you can, but the point of using separating funnel is to make work easier, hence u wont need to transfer the organic or aqueous layer by transfer pipettes or other ways. 

Yes of course we can do it. The separating funnel is only used for ease in operation normally when we need to separate the two phases

I have used a beaker with a magnetic stirrer for solvent extraction tests.  Much easier to do larger scale tests, or where pH measurement and control is required.  Care should be taken in the speed of stirring, but once set it can be maintained which aids in repeatability.  For kinetics a syringe can be used to take a sample while still mixing.

A big plus is air entrainment can be lessened which is a big issue in the clean phase separation in a flask.  Also the continuous phase (which the other phase is dispersed in) can be controlled, in a flask this is a more random situation due to the mixing.

The most convenient, if small volumes are concerned, is extraction in test-tubes. We use test-tubes with 10 ml volume, shaken on horizontal shaker in termobox, and after shaking the tubes are placed into centrifuge for short time in order to perfectly separate phases. The aliquots are withdrawn with Eppendorf pipette.

yes we can use beaker for stirring with magnetic needle however the separating funnel need to separate two layer 

Bundle of thanks

I have also a question that if we use magnetic stirrer then how to take the sample of aqueous and organic layer separately by syringe.