Captain reported a Door Open Warning in flight. While attempting to verify the door was closed; the door blew open and separated from the aircraft. The Captain performed a diversion and made a precautionary landing.

Narrative

After the previously reported rejected takeoff; I received re-release and prepared for departure again. Having just experienced the door opening on the takeoff roll due to what I assumed to be personal negligence in verifying the door's closure; I checked and triple checked that the latches were fully engaged. In the initial climb phase of flight I noticed a hissing noise; and felt air coming in through the crew door. I pulled on the door handle to see if the door would seal better; but when I let go of the handle; the door opened violently and came off at the hinges. This happened at about 3000 ft. MSL a few miles south east of ZZZ. The wind blew my headset off and was causing papers and loose objects to fly around the Cockpit; so I reduced power to slow down and mitigate the wind in the Cockpit. I did not initially adjust trim enough which caused a descent to about 2600 ft. MSL while I found and donned my headset; at which point I informed approach that my door had fallen off and I would be returning to ZZZ1. I initially became aware that something was not quite right when I could hear and feel air coming in through the door during climb. I believe there was a mechanical failure with the door latch mechanism. Immediate air return to ZZZ1. Perhaps the door would not have opened if I had not attempted to pull it tight when I realized it was not sealing properly. All I can think of is that by doing so; it relieved pressure off the hooks and allowed them to fall back enough that they could not engage properly when I stopped pulling on the door handle. If a similar situation occurred and I noticed air coming in through the door; I would not touch it at all and return preemptively to have the door inspected.