She is not elected and does not have the authority of the people behind her. The Mayor must do his own job, the one he has the legal authority to do.
You obviously have not seen the videos. You should watch the video of the meeting, or at least, the shorter video of the incident. I couldn’t believe what I saw on the shorter video, so I watched several meetings, trying to understand.
Ms. Jones was speaking during her turn at the “call for citizens” portion of the meeting, with the approval of the chair of the meeting. She had the floor, at the recognition of the chair, the mayor. She did not violate any rules.
The mayor and Ms. Jones were interrupted by a council member, who initiated the anarchy at the meeting ( several times, in fact). The chief obeyed out of order councilman, rather than the mayor - who, again, had the right to recognize speakers in the meeting.