Hiss is usually a signal noise issue but without any input and/or the unit in tuner MUTE mode there should literally be 0 output from the GT-10B. So I'd start to blame the mixer, maybe it simply has noisey preamps? Most mixers bypass the channel preamp when running 1/4" instead of XLR. You can also just plug an unconnected XLR into the mixer on that same channel to see if the mixer channel has some inherent noise.
If none of that pans out eliminate the MIXER from the equation and try a different source to send the GT-10B to. Run 1/4" into a FX RETURN or POWER AMP IN on a bass amp. Run the XLR straight into the XLR input on a PA power amp.
Some other ideas would be to try some of the other outputs from the GT-10B just purely for troubleshooting.
* Use the FX SEND. Try placing it at the beginning and end of the signal chain just to see if that has any bearing.
* Install the USB driver and run USB to your computer and into some recording app. Now try with the DGT block at the beginning and end of the signal chain just to see if that has any bearing.
* Check the headphone output which should be the same thing coming out of the 1/4" and XLR but pushed through a headphone amp so that should theoretically be the noisiest possible output on the unit.
Trying the FX SEND theoretically eliminates the final D/A conversion so you're isolating that portion of the unit. Note that it's sending instrument level signal not line level to my knowledge, though you have control over the FX SEND LEVEL to compensate.
Beyond that I'd phone Roland support. Their phone support is pretty good, they often bust out a unit while on the phone. Totally skip their email support though, it's very poor due to their horrible helpdesk interface. You get like 220 characters to enter your text, they send a short reply and instantly close the ticket, you cannot reply directly to the ticket and have to start a totally new ticket. Then they usually just tell you to phone support because it's impossible to have a detailed conversation via their crappy helpdesk system.

It'd madness.