Proxmox partitions it's storage with lvm. While there might be more than enough storage on your disk, possibly there is not enough on the partition you are copying to, i.e. the root partition is usually quite small.
In your case I would recommend mounting the storage where your vmd is via sshfs or something similar and importing it with
qm disk import
plus the respective parameters directly over sshfs. This will import it into whatever storage you are using for disk images, usually local-lvm, the partition that is using up the rest of your disk