Shutdown as many services as you can, on the running system

I am using /dev/sdk for the device of the new disk, in these examples.

Mount the new disk to /newboot

cp -axv / /newboot
cp -av /dev /newboot

edit the /newboot/etc/fstab with the new uuid of the new boot disk


Copy the MBR from the old drive to the new.

if=/dev/sda1 of=/dev/sdk1 bs=512 count=1

Install grub on the drive

grub-install --root-directory=/newboot /dev/sdk


Check the /boot/grub/grub.cfg file and make sure the UUID of the new partition is correct. If it is not replace it with the UUID of the new boot disk.