In general, I have to mention that such operation is not supposed to be performed as it may cause various issues, so any further advises are supposed to be taken at your own risk.
With packages easiest way is to create symlink of Data directory to new disk. Here is how this can be done, for instance, when moving Data to /mount/sdb:
Prepare server backup so that in case of unexpected issues you will be able to rollback to previous server state;
Execute following script to shutdown Document Server:
Transfer /var/www/onlyoffice/Data directory to /mount/sdb/ with mv /var/www/onlyoffice/Data/ /mount/sdb/ and grant proper rights to new destination with chown -R onlyoffice:onlyoffice /mount/sdb/Data;
Create symlink:
ln -s /mount/sdb/Data /var/www/onlyoffice/
After this step check if symlink is created with ls -lai /var/www/onlyoffice/.