Could you please post screenshots (or a sketch/mock-up) with the pertinent Panels (Toolbar, Layers, Options Bar, …) visible of the original image and the three resulting images?
If you mean three documents, you can use the canvas size command, three times with different anchor points for top-centre, middle-centre and bottom-centre. You may wish to be pixel-precise rather than using 33.33% as the canvas size value, which could mean that one of the three tiles is sized a little different to the other two.