Albert Barnes on Mark 8:12

Sighed deeply in his spirit. His soul, his heart, was deeply affected at their wickedness and hypocrisy. The word spirit, here, means human soul. He drew groans deeply from his breast.

No sign be given. That is, no such sign as they asked--to wit, a sign from heaven. He said a sign should be given, the same as was furnished by Jonas, Mt 16:1. But this was not what they asked, nor would it be given because they asked it.