Is there a way for black to stop checkmate?

Black to Play. Can he stop the checkmate? 
 

I don't think so. Looks like black got into a pretty bad position. I might try some sort of swindle with ...Qh4, hoping white's totally not expecting an extra move. If I had to do something. But I don't think it changes anything.

Does black have a miracle save here?

Sure, qg8.  Bxq, kxq, bxp, kxp, qh7, kg5, and black is still probably getting mated in a few moves and down material to boot, but at least white has to work a little. 

... Qg8

Bc1 Qh7

Qxh7 mate.

=)

Ne6

... Ne6

Bxg7 check Kxg7

Qh7 check Kf8

Qf7

It still won't work if Kg8. Qh7 would still be mate.

what about Nd4-e6   ?

1... Ne6 2.Bxg7+  Kxg7 3.Qh7+  Kf6 . How does white reply?

1...Ne6 2. Bg5+ Kg8 3. Qh7+ Kf8 4. Qh8+ ?

... Ne6 is the best hope that White will mess up. Then Bg5+ to cover a flight square, which actually is something White has to find, followed by ... Kg8; Qh7+Kf8; Qh8 mate.

OTOH, If  ... Ne6;   Bxg7+?  Kxg7;   Qh7+  Kf6 steps forward and there is no mate in sight (though Black is so inferior he certainly will be mated eventually).

So ... there is no way to stop the mate versus best play but one can make White prove it.

Okay. A challenge for anyone who wants to do it. See if you can back trace the position and figure  out the whole game from move 1.