Why does OS X delete files directly without moving them into the trash? On an external HD, when I delete a file, OS X prompts me that the file will be deleted without putting it into the trash folder.
What is the reasons for that?
How can I move it in trash folder before permanently delete it?
The OS X finder maintains a few hidden directories to handle Mac specific filesystem functions like:


Spotlight = /Volumes/X/.Spotlight-V100
file version history = /Volumes/X/.DocumentRevisions-V100
trash = /Volumes/X/.Trashes
Time Machine (and other) filesystem changes = /Volumes/X/.fseventsd


These are suppressed on many network and "foreign" filesystems by design and/or if the filesystem is read-only. You can use the command line tool (or the get information menu command in Disk Utility) to inspect the format of your volume:

diskutil list /Volumes/X/


Hopefully this is the cause - if your volume is of type Apple_HFS or similar and you don't see the hidden directories, you might need to dig deeper and repair that filesystem or look at some other cause. The simple reason would be that the hidden directories are suppressed by design in your case.