dan.tillin,
You need to first remove all the Mule related components that are added to the profile and then only you can remove the Mule Studio plugin.
Please take a look at the screenshot for your visual reference.
Our latest version is MyEclipse 2014, based on Eclipse Kepler (4.3). I suggest you download and install MyEclipse 2014 alongside your existing MyEclipse 10.7 install and give it a try, as it has many bug fixes and new enhancements. Please take a look at this link for more information on MyEclipse 2014.
Let us know how it works for you.