This requires a brief anatomy lesson, plus a bit of freehand drawing skill.
The jawbone is essentially a hinge that pivots on the skull. The pivot point sits very near the earlobe. (See area below shaded in red.)
You need to find the jawbone on the profile photo that you want to edit. The jaw obviously includes the chin and lower teeth, but on the rest of the face there is skin and muscle that moves and stretches as the jaw opens. Therefore your selection of the entire jaw doesn't need to be anatomically perfect. Something like this is good enough.
Copy the jaw portion of the subject onto a new layer. Use Edit>Transform>Rotate to tilt the jaw down at the chin. Then use the Move tool to put the pivot point back where it originally started—just below the earlobe.
Use a layer mask to clean up any obvious seams.
When you open your mouth, your upper lip (at the corner of your mouth) is stretched downward. Use the Liquify filter on the upper lip to indicate this.
Depending on your artistic ability, you may possibly see teeth and the tongue once the mouth is open. But a quick and dirty way to indicate the open mouth is to fill it with black.
Here is my lightning-fast two minute version of this.