Clone whole partition or hard drive to a sparse file

You want dd_rescue.

dd_rescue -a -b 8M /dev/sda1 /mount/external/backup/sda1.raw

Just for completeness the call for ddrescue. The --sparse or -S flag allows the destination to be written sparsely:

$ ddrescue -S -b8M /dev/sda1 /mount/external/backup/sda1.raw

Or with long option:

$ ddrescue --sparse --block-size 8M /dev/sda1 /mount/external/backup/sda1.raw

Or if you prefer MiBs:

$ ddrescue -S -b8Mi /dev/sda1 /mount/external/backup/sda1.raw

To allow the rescue to be interrupted and resumed, you can also make use of a logfile:

$ ddrescue -S -b8Mi /dev/sda1 /mount/external/backup/sda1.raw ~/sda1.rescue.log

Note that GNU ddrescue and dd_rescue are different programs. But GNU ddrescue seems to be more widespread. For example it is already packaged with GRML.

There was a patch offered in 2007 to provide sparse file support in GNU dd, but it looks to have not made it into coreutils (at least not as of 8.4). I doubt dd has changed too much since then, the patch might apply against the current version without a lot of work.

I'm also really impressed by the creative use of cp in your question, and it got me on the track of using it to accomplish resuming (here resuming from ~80M into the source):

cp --sparse=always \
  <(dd if=/dev/sda1 bs=8M skip=10) /dev/stdout \
  | dd bs=8M seek=10 of=/mount/external/backup/sda1.raw

Edit: scratch that. The second dd would of course be seeking to the wrong position in the output file, since it's not the same length as the input.