The ground is tied to the chassis ground. In the event of a fault the ground protects you in the event of a fault. Do not disconnect the ground. Another problem would be protecting your scope, with the SMPS disconnected, the fault would run through the prove ground and scope, then to ground. With sufficient current, this would probably smoke the probe and maybe the scope, then you if you touched the chassis.
Source: SMPS power supply
If your talking about disconnecting the ATX ground from the motherboard connector, then the motherboard will not function and the PS won't turn on.
Your right that you are creating a ground loop, with the o-scope ground, but there are better and safer ways to make a measurement like this.
The best (and most expensive way) would be to use a differential probe
A way (that can also be dangerous depending on the voltages involved) would be to use an isolation transformer:
This topic has been discussed multiple times before, isolation transformers are not magic safety devices - do not trust them blindly, use differential probes.
Isolation transformer has one meaningful use with oscilloscopes, but it is still dangerous.
As oscilloscope and DUT are both grounded, you can only clip
oscilloscope ground clip to the earth and measure signals with respect
to the earth. This may not be what you want. If you power DUT from
isolation transformer, you can clip oscilloscope probe ground clip
anywhere and measure what you want. However, by doing this you once
again make DUT referenced to earth (floating becomes earth referenced)
and DEFEAT RCD/GFCI PROTECTION FOR DUT. See simplified diagram. Note
that GFCI/RCD is not effective in this configuration even if you add
it after isolation transformer.
Source: EEvblog user:electr_peter
As anecdotal evidence from a reprap that has tried this see this warning (I think the spelling reflects on the smarts that it would take to do something like this) :
I just plug ghe (sic) ATX power supply to an outlet with no ground
wire. During a print i acidentally touch the atx power supply then i
got electric shock
Just a warning to all do not leave ground wire floating. Btw. My power
is the 550w supplyed in the kit