In order to achieve this it would be necessary to do it on single user mode or using a LiveCD, that's what you'll find on internet.
Furthermore, it's possible to perform this at runtime (a little bit risky, of course) but I think this way will only work for /var and not for /usr, some runtime libs depend on this folder. You can try on a test machine previously if it do works.
First at all you must check that any process/services is using/writing to the directory you want to move.
lsof | grep -E '/usr|/var'
Generally /var is still in use for pid and sock files, /usr as well as any lib will need it.
So, stop/kill services and processes that appear.
COMMAND PID TID USER FD TYPE DEVICE SIZE/OFF NODE NAME
cupsd 723 root 5u REG 8,1 0 8651393 /var/log/cups/error_log
cupsd 723 root 6u REG 8,1 0 8651908 /var/log/cups/page_log
cupsd 723 root 12u unix 0xffff88020d97d780 0t0 9958 /var/run/cups/cups.sock
In this short example, cups daemon is running and using those directories. If stop them, they will not appear on lsof output.
After that, you need a copy of your current data, I'll suggest using rsync instead of cp (in order to preserve everything, permissions, symlinks, etc.)
Do your backup
rsync -avz /var/* /mnt/var
rsync -avz /usr/* /mnt/usr
rsync -avz /mnt/var/* /var
rsync -avz /mnt/usr/* /usr
Edit your /etc/fstab file and comment/delete the entries where /var and /usr where supposed to be mounted.
Then you can start all services you stopped or restart your machine. If for /usr doesn't work, you can't stop a daemon (maybe you can't kill it cause depends on init pid) the only way will be using a LiveCD.
Though you didn't mention which type of machine is (your PC, office machine, a server, etc) it will depend on this to do perform the formal way possible.