Modern playline Barbies' heads are best removed with heat.
Have a thin flat-bladed screwdriver, a nipper/button shank cutter (
like this one and a hairdryer on hand.
Aim the hairdryer at the base of the head, where it meets the neck. You'll want to aim it at a couple of different spots around the neck opening, try about 20 seconds total to start. (Depending on the doll and the hairdryer) It does take a couple of heads to get a feel for when the vinyl is soft enough, so you may want to try another victim/subject or two first.
The connector in most modern Barbies' heads is some variation on an anchor.

(Quick 'n' dirty illustration, sorry)
When the vinyl has softened a bit, squeeze the head so that you can slip the blade of the screwdriver between the head and the neck. Pull and pry until you get the neck opening pulled up over the base of the 'anchor'. Now slide the nippers in and snip the connector at the marked spot over the base of the anchor.