As I mentioned in a previous discussion, this new design tool was intended to be used on a desktop computer. If you’d like to use a cell phone we’d recommend using our mobile website, which was designed for use on small screens such as cell phones.
However, for completeness, I did check the desktop website on a mobile phone and I still see the full context menu. Trouble is, it’s hard to see the full menu because there simply isn’t room on the device to display the full menu.
I’ve passed along a suggestion to add copy/paste to the mobile website.