Moving my music to external drive. Can I then delete it from my laptop

This may seem like a silly question, but......when I drag my file containing my music over to my external hd, it seems like it just copies rather than actually moving the stuff off of my laptop hd. to the external hd.

I am also having the "missing dll file" issue so I am going to un/reinstall. Once I determine that itunes can retrieve the music from my external drive, can I then delete it from my laptop since the whole issue is that my laptop has no space?

Thanks in advance. I have been at this for hours upon hours. I miss DOS!!😕