It is not possible to delete multiple features at once through the user interface in ArcGIS Online. This is by design.
However, there is an alternative of doing so from the REST URL. Features in a service can be edited using supported operations from the ArcGIS REST API, which accesses the underlying framework of ArcGIS Online. These supported editing operations include Create, Update, and Delete functions. Users can do batch deletion using Delete Features by the Object IDs.
To delete multiple features from a hosted feature service using the ArcGIS REST API, follow the steps below:
There is another alternative to delete multiple records in a feature service using ArcREST. The following link is a sample of Python script to delete rows from a layer: delete_rows_from_service.py.