You've put this question under 'learning Japanese', but I'm guessing it's about English rather than Japanese. 'His face dropped' - or more commonly 'his face fell' - means that his facial expression suddenly changed from looking happy to looking sad or disappointed. If you think of the transition - from bright eyes and smiling upturned mouth to downturned eyes and sad-looking mouth - you can imagine what why we say 'dropped' or 'fell'.

It's like he became sad rapidly. Example; I was happy because I was eating these awesome chips then the chips all fell to the floor. So I went from =] to =[

I wonder if its something like to appear ?