Virtualizor has an option to migrate a VPS/container from one server to another within the same Virtualizor cluster.
Depending on Virtualization present on the server, you can choose between Live and offline migration.
Offline migration option is supported on all types of Virtualizor except XenServer.
This type of migration will stop the VPS during migration process.
You can view this guide for more information :
https://www.virtualizor.com/docs/admin/offline-migration/
Live migration option on Virtualizor panel is only support for KVM Virtualizor.
If you have configured shared storage in backend and selected source and destination server for storage on Virtualizor panel then you can choose 'Shared storage' option for migration so that it does not attempts to migrate the VPS disk as well.
You can view this guide for more information :
https://www.virtualizor.com/docs/admin/live-migration/