If you can't get things fixed on the container, you could try the following...
CTID=336
mount proc /vz/private/$CTID/proc -t proc
mount sys /vz/private/$CTID/sys -t sysfs
mount --bind /dev /vz/private/$CTID/dev
chroot /vz/private/$CTID
You should be chrooted into the container's root with everything mounted that you would need to start up mysqld manually and dump whatever you need.
Once you're done, just make sure to exit out of the chroot and unmount everything...
umount /vz/private/$CTID/dev
umount /vz/private/$CTID/sys
umount /vz/private/$CTID/proc
Hope that helps!