"Chagrin" means to be annoyed or distressed.

Option A: Intense happiness or excitement, often overwhelming. 

Option B:   The act of calming or soothing someone, often to reduce anger.

Option C: Joyful delight or amusement, often with a sense of mischief.

Option D: Deep embarrassment or stress, often due to humiliation.

Of the given options, Mortification works best as a synonym for chagrin. 

Hence, the answer is option D.