Hi Roni! Julianne from Mixpanel Support here.
If you want to stop Mixpanel from populating the $city property on future events, you can disable IP-based geolocation for the events you send. That prevents Mixpanel from adding the location-derived fields. For the JavaScript SDK, you can do so by setting ip: false in the config. Note: geolocation is treated as a set, so disabling it will remove the other location fields as well.
Would that work for your use case?