Define “super slow”? Did you run any sort of benchmarking software (like Crystal Disk Mark: http://crystalmark.info/?lang=en) to determine the actual read/write speed you were achieving across your local network?
Before opening up the enclosure to remove the hard drive you may want to take a moment to read through the following discussion:
Its important to understand what the My Cloud is. It is a network attached storage device. Your copy speed will be dependent on several factors including your computer/device hardware, your local network setup including the use of or lack of using Gigabit networking, using WiFi, etc. Often slow copy speeds can be attributed to not using Gigabit networking and copying across a WiFi connection.
If you do decide to remove the hard drive from the My Cloud enclosure than as indicated above you can use the Paragon EXTFS driver to read the Linux formatted partitions on teh My Cloud drive to copy the data off the drive, then re-partition and reformat the drive into a more suitable format like NTFS if using Windows. Often people will use a Linux boot disc/live CD (like that from Ubuntu for example) to read and backup the drive once removed from the My Cloud.