Did the Queen of Hearts say 'off with his head'?

Yes. Several times.

The players all played at once without waiting for turns, quarrelling all the while, and fighting for the hedgehogs; and in a very short time the Queen was in a furious passion, and went stamping about, and shouting Off with his head!' or Off with her head!' about once in a minute.

The Queen had only one way of settling all difficulties, great or small. Off with his head!' she said, without even looking round.

All the time they were playing the Queen never left off quarrelling with the other players, and shouting Off with his head!' or Off with her head!'

Well, I'd hardly finished the first verse,' said the Hatter, when the Queen jumped up and bawled out, "He's murdering the time! Off with his head!"'