Along other aspects of Edit Mode reorganisation in Blender 2.80, Separate, the ability to detach a selection as a fully independent editable object, has been moved from the Vertex sub-menu to the main Mesh menu of the 3D View.
In Edit Mode, to Separate a selection choose the elements to be included in the resulting new object and from the main Mesh menu (upper-left), click Separate then an appropriate option – Mesh » Separate » [option] (or press P to display the Separate quick access menu);
- Separate: detaches the selected elements.
- By Material: detaches based on/per material assignments.
- By Loose Parts: detaches based on connection to other elements.
Design note: the resulting object will comprise whatever was selected, vertices, edges or faces. It will also duplicate the Origin point associated with the parent object (which may need adjustment as needed).
Depending on the option selected a new object will be created, the remaining structure left in place.
Editing Separated Object
As selections detached in this way create distinct independent objects, to edit, exit Edit Mode for the selected Object (Tab), select the new and toggle (Tab) back into Edit Mode to work on the new mesh.
Design note: to include the new object as part of a multi-object editable group, exit Edit Mode (Tab) and select it before toggling back into Edit Mode to continue working on both mesh objects at the same time.
The new object can be edited on its own or included as part of a larger editable group with multi-object editing.