Windows Server 2008 R2 provides functionality that adding or removal of virtual storage to the virtual machine while it is in operation. It refers to as "hot add".
There are two controller types of virtual hard disk on Hyper-V. The one is IDE controller type that is used to boot virtual machine and the other is SCSI controller. This SCSI controller type supports "hot add" or "hot removal" of virtual hard disks.
1. To add virtual hard disk to VMs, SCSI controller must be added to a virtual machine.
2. Left is configuration window of a VM and right one is Disk Management console in the guest OS of the virtual machine. Looking at the right, there are three hard disks on the list. - Two partitioned disks (C, D) and the one is a system-reserved disk.
In order to add a new one, it needs to make a virtual hard disk, and then attach it to the VM.
3. On the right window, the new hard disk which its status is unformatted and unallocated has been added.
4. It stars format of the disk. On the contrary this example, if you attach a formatted disk, you don't have to format again the disk.
5. After the format is completed, you can see that letter E is allocated to the drive.
This is so-called hot add of virtual storage without any shutdown of VM on Windows Server 2008 R2 Hyper-V.
5. How about hot removal of VHD? You just click "remove" button on the configuration window of VM.
These links are topics related hot addition / removal of virtual storage.