I am interested in image the internal HDD and backup just the filesystem file as backups. My external HDD is 2TB while 100 GB is only used in my internal HDD. Both methods are welcome here.
Code and situation
$ ls -la /dev/sdb
brwx---rwx 1 root disk 8, 16 Jul 13 10:44 /dev/sdb
$ sudo chmod 777 /dev/sdb
I start the Backups program in GUI of Debian 8.1 which is probably Deja Dup.
I set the Buffalo 2TB disc the back file disc.
I run backup but I get this window about permission denied although I have 777 as permissions.

The command mount gives this output
/dev/sdb1 on /media/masi/_linuxDisc type xfs (rw,nosuid,nodev,relatime,attr2,inode64,noquota,uhelper=udisks2)
Changing permissions after mjturner's answer
$ ls -la /media/masi/_linuxDisc/
total 4
drwxr-xr-x 2 root root 6 Jul 12 19:42 .
drwxr-x---+ 3 root root 4096 Jul 13 10:44 ..
$ sudo chmod 755 /media/masi/_linuxDisc/
[sudo] password for masi:
$ ls -la /media/masi/_linuxDisc
total 4
drwxr-xr-x 2 root root 6 Jul 12 19:42 .
drwxr-x---+ 3 root root 4096 Jul 13 10:44 ..
which shows no effect of chmod. Why?
How can you set correct permissions for the backup in Debian 8.1?