What you are experiencing is bad subframe bushings. I had to take my car in 3 times before the service manager figured out that Mazda had TSB out for this issue. It usually happens when the car sits for a little bit. I would get that noise while backing out of my driveway making a hard right. I actually had my subframe bushings replaced Friday and no longer have that issue.
2010 MazdaSpeed 3 Tech Package
Current Mods - CP-E Turbo Inlet Pipe, CP-E cel Intake, HKS BOV, 5000K Extreme HIDS, Nokya Hyper Yellow Fogs[/FONT]