Mac Pro 2013 keep freezing

Its been a while i'm searching a solution for this.

Since I have my new Mac Pro (February 27th) it keeps freezing. I can still move my mouse, music keep playing, but i can't do anything else. I have to reboot manually the computer. I called Apple Care 3 times. Did a PRAM reset, verify & repaid disk, format the Mac but the problem is still there.

its random and i can't put the finger on what's going on.

At first it was just freezing. But a month later, screen started to "glitch", like the graphic card was about to die. I'm using the same material than on my other Mac (screen, mouse, external hard drive, keyboard etc.) The only thing i change its the computer. Everything was fine BEFORE.

I thought it could be my external hard drive (because it was always open for Time Machine and get my backup files from my older Mac). I verify the disk, the firmware, but evrything was OK. So I turn it off and everything was fine for about 8 days. Open the computer this morning, turn on the External Hard Drive and 15 min later, it froze. I emailed LaCie company, made some verification with them, they think it could be the cable. I turn my External Drive off and continue my work. Thought after 2 months finally i was over with this.

Unfortunately, the Mac froze again 4 hours later.... but the External Hard Drive was off...

I can't find any pattern. I had the same app opened as usual (thunderbird, transmit, itunes, chrome, sublime text,skype) nothing to crash a brand new Mac Pro.....

Honestly i'm very disappointed.

Anyone have an idea ??