Is there a way to travel from Changping to Chengde by train?

Yes, you can take a direct train from Changping Railway Station. The train departs at 10:45, and the trip takes about 9 hours. A hard seat costs CNY 21.5.

I am sorry that there is no train service to Mutianyu Great Wall. You can take bus line h54 to Huairou North Avenue Station. Then, change to bus line h23 or h50 to Mutianyu Roundabout. Afterwards, walk north to the ticket office. :)