I have the apps for Time, People & Sports Illustrated and would like to know if I can delete the issues when I am done reading that copy ?

Bumped you into the App section, as you are more likely to receive a response here.

I don't own those apps, but the two standard ways of deleting documents on the iPad are:
a) swiping across the magazine and then press delete
b) pressing onto the magazine for 1-2 seconds and then select the x

However, it is entirely possible, that those magazine apps have no proper delete function.

I am having same issue (no pun intended). Takes up too much space, I would love to delete old issues. Anyone else have any ideas?

Just tried this based on earlier answers. Open up the library, place your finger on one of the issues and hold (as you would when organizing your apps) then hit the 'x' and you're done.