You say it shows up in Disk Utility, but doesn't mount? What does Terminal say is the Device Identifier in Terminal? The command to check is "diskutil list" (without the quotes). It'll then list all drives connected to the computer and their partitions. It'll have your primary drive as well, so keep an eye on the drive's name. It should be something like
/dev/disk0 and the partitions will be sequencially identified as disk0s1, disks2, etc. You're wanting the /dev/disk# info for the Passport Ultra. Once you get that info I can tell you how to copy a drive/volume/partition without it being mounted by the system. But it'll take some Terminal work if you're comfortable with it