WD My Cloud crashes in few minutes after having attached USB HDD (My Book or Seagate)

My Cloud OS 3 Personal & Network Attached Storage My Cloud
4

I suspect the difference is not the powered/unpowered nature, but the size.

Adding a large HDD to the USB port is likely to start indexing all that data, which may bring the MyCloud to a grinding halt, so that it appears to crash.

This may be of help:

http://community.wd.com/t5/WD-My-Cloud/Hidden-wdmc-directories-created-by-mcserver-and-photodbmerger/m-p/682091

Alternatively, there have been many reports of problems with the USB interface; have a look through the forums for similar threads.