The officer handled this arrest effectively.
For a suspect involved in a violent crime, yes. For a passive but uncooperative student, not so much.
According to the school's own
handbook (PDF), violations listed as “disruptive behavior” and “refusal to obey,” which they say the girl was charged with, carry the consequence of detention or in-school suspension. The only two behaviors listed in the handbook that can result in arrest are 1) fighting and 2) verbal confrontation, neither of which the sheriff or school administrators alleged the student had committed.
It never should have gotten to the point of an arrest even being considered, as the student was not a danger to herself or the other students, was not fighting or verbally confronting anyone. What they should have done is giver her a choice, "Either come with me to the office to talk about your behavior, or you can refuse to come to the office and just sit here quietly and continue to rack up days added to your suspension." Then, if she didn't sit there quietly, or continued to sit there by the time class was over, they should have given her a choice of standing up and coming with them, or they would remove her and her desk from the classroom.
Instead, the SRO grabbed her by the neck (the maneuver that got him fired, most likely), flipped her over and body slammed, yes, body slammed her to the floor, dragged her out of the chair, flipped her over and handcuffed her. That cannot be defended.