Create the two split image layers and save them out. You can use menu File>Scripts>Export Layers To Files to do the save them out part. Photoshop ships with the Export Layers To Files.jsx script.
Here I created a selection around the face and added it as a layer mask. I duped the layer and inverted the layer mask ans saved the layers out as jpeg files and opened them. Had I saved the as png the face file would be just the face with no border and the head image would have a transparent area where the face should be.
Draw a marquee around the first image. Right Click > Layer via cut. This cuts the first image from your main layer and puts it on a new layer. Select both layers (shift+click). Right Click > Link Layers. Go to Layers menu > Align > Top Edges. Repeat with Align > Left Edges. Crop and save.
File > Scripts > Export Layers to files.