Have you taken a look at the following thread that explains many of the copying speed issues:
https://community.wd.com/t/before-you-pack-up-your-wd-and-return-it-lets-talk-about-copying-speeds/91887
Have you performed a 4 second reset via the reset button the back of the My Cloud? What about a 40 second reset?
How are you transferring the files (what program/app), and with which OS? How is the computer connected to the My Cloud, via Wi-Fi?
To answer your specific question, yes one could disassemble the My Cloud and remove the SATA hard drive within it. One would have to reformat the drive however since it is typically subdivided into 8 partitions with the data partition being the fourth partition. Because the My Cloud uses Linux for its operating system Windows may not be able to read/access the various partitions without 3rd party software that can read/access EXT4 and other non Windows hard drive formats.
Note: Disassembling the My Cloud will probably void the warrantee on both the My Cloud and the drive itself.
