There is a place in South Phoenix called Industrial Metal Supply located at 5150 South 48th Street, Phoenix, AZ . That's just west of Mesa on the other side of I-10. I think they are open on Saturday Mornings. They sell mostly new stuff, but have lots of cutoffs at very reasonable prices. They also sell most sizes of brass rod, aluminum rod, and cold rolled steel in 12" lengths. They do cater to the small buyer as well as businesses.
There's also a place called Apache Reclamation which is kind of a an industrial surplus store. It's right of I-17 at about 3rd St or so... pretty close to Mesa. Lots of cool stuff there, but take your paper towels... you'll get real dirty there and they are open on Saturday until about 1pm.
The only other place I know of is Davis Salvage on Washington St near 34th st. I think they also are open on Saturday mornings.
Of course, I did move away from Phoenix 2 years ago, so I don't know if these places are still in business or not, but assume they are since they've been around for years.
Chuck