Yes, Donald Trump will have the power to destroy net neutrality. Trump will assume office with all three branches of government controlled by Republicans. Since the aim of Republicans is to amass power in the hands of the rich at the expense of the poor and middle class, there will be no problem for him to get rid of net neutrality.
Yes, Donald Trump does have the power to destroy net neutrality. By simply appointing a new chairman of the Federal Communications Commission who would not enforce current policies prohibiting discriminatory fast lanes, Trump could effectively open the door for the largest cable and phone companies to circumvent unfettered access to the Internet.
Donald Trump does not own the Internet. He does not have a kill switch. If he wants to make any changes to net neutrality, he's going to have to get through Congress. Of course, where Congress is concerned there are a lot of lobbyists that will also make sure they get to have a say.
There are many factors that combine to result in net neutrality and the fair treatment of data. It is not up to the president of the United States alone. Donald Trump has not indicated any intent to destroy net neutrality and would not have the authority to do so by executive order.