The other responses assume you mean remove the TAPE, not the DRIVE. If that assumption is correct, then yes you can remove the tape pretty much whenever the drive will let you.
If you mean remove the DRIVE, then no you cannot remove it without powering down. Even if the drive is in an external bay and connected to an external SCSI connector, I strongly advise against just removing it while powered up. AFAIAA, no external SCSI connectors are hotswap enabled.
only the SCSI-3 specification is capable of hotswapping. However, you need the device to be connected to a hotswap-capable backplane. The external connector on most SCSI cards does not constitute a hotswap backplane. AFAIK, hardswap backplanes are only available for hard drives (SCA - 80 pin SCSI, those new small drives Sun uses, and SATA.)
Edit : new small jobbies Sun uses are called SAS drives. They're the size of notebook hard drives (2.5") and spin at 10k or 15k rpm.
If its the only device on that channel then hot-swap it. You just have to do a scan for new hardware once the new drive is in. PS - Always remove power first.
The hadware can handle the hot-swap, its the OS that clutches, so make sure nothing is trying to access the drive at the time, or you might just have to reboot anyway.