Can the MH-60 helicopter fly without one or all of the stabilators?
Assuming there is no STC ("Supplemental Type Certificate") that addresses this as an existing modification, the answer, in terms of acceptable aircraft airworthiness, is a hard no.

"Can the aircraft fly" is a tricky question in some ways, but dead-easy in others.  And remember: a helicopter is a thousand moving parts spinning wildly around an oil leak.  

If you're looking at it from a flight physics and dynamics perspective, as a result of a mishap/damage in flight, (assuming no other problems like a damaged rotor or loss of hydraulic fluid,) and whether you can control the aircraft safely to the ground, a skilled pilot rated for this aircraft "type" would probably be able to wrestle the aircraft to a safe landing.  The main rotor does the work of holding the helo aloft, and the tail rotor holds the attitude steady against the torque of the main rotor.  The stabilator (stabilizer-elevator combined surface) does not contribute to total lift in hover, although it may affect lift in forward flight.

However, any mission the helo had been in the midst of should be immediately abandoned for the sake of making the landing.  Even if you were rescuing someone from drowning in the ocean, you're more likely to just add the flight crew to the tally of the dead if you persist in trying to make the bird work while in an adverse configuration.

This does not answer what an actual pilot of that type - which I am not - would experience in flight.  But the stabilator is considered a flight control surface, and you never take to the air without your flight controls 100% operational.

But ending up missing part of your flight control surfaces during flight would be considered an emergency condition.  If instead the aircraft is already on the ground, in need of maintenance, and one is considering a "ferry flight" to somewhere else to better service it, there are many things that an inspector could let slide for just a ferry flight, but this is not one of them.

Such a stabilator contributes to the control, stability, and balance of the aircraft, and without the entire stabilator, the aircraft is not in flight configuration, and therefore, it's not "airworthy".

Definition of Airworthiness: 


  The aircraft conforms to its type design and is in a condition for safe operation.


Source: 14 CFR Part 3.5(a)

Even if a cogent argument is somehow made that the helicopter is "in a condition for safe operation" while lacking all or part of its stabilator, it still utterly fails the first half, being: "conforms to its type design".

A note regarding balance:  
Many mid-sized helicopters have an acceptable CG (Center of Gravity) range that's about the size and shape of a large mobile phone (as I write this in early 2016).  This is a larger craft, flown by the military, so its CG envelope may be the size of a small to medium tablet device.  Loading various people near the CG location doesn't shift the CG very much, which is why the main passenger/cargo area is always under the main rotor.  But that stabilator flight control surface could weigh 20, 50, 100 pounds or more, and removing that from the end of a long lever arm at the end of the tail boom will cause a noticeable shift in CG location, possibly putting it out of range for the aircraft.  This is also a situation that a skilled pilot in an emergency may be able to compensate for if action is taken immediately, but is a condition you never enter into knowingly. That way lies only heartache and doom.

I am an FAA certified A&amp;P (Airframe and Powerplant) mechanic, and during my training school, the third-ranking member in the entire FAA (in 2007) came and gave a talk on a few different topics, but primarily on the concept of airworthiness.  It comes down to this:  Are you SURE it will fly safely?  How sure?  Would you put your kids in that aircraft and let it fly?  As aircraft mechanics, we need to be that sure that the aircraft is safe to fly, or, it simply isn't. 


  An aircraft is fully airworthy, or it's not airworthy.


The Sikorsky SH-60 Seahawk, without a complete stabilator, is not airworthy.