Try to use such next function for such situation:
copy_wdir() { mkdir -p -- "$(dirname -- "$2")" && cp -- "$1" "$2" ; }
and use it as
copy_wdir aaa/deep/sea/blob.psd bbb/deep/sea/blob.psd
By the way, GNU `cp` has a `--parents` option. It's really close to what you want, but not exactly.
It will also create `aaa` directory that seems you don't need. However you can first cd to `aaa` and copy like:
cd aaa && cp --parents deep/sea/blob.psd ../bbb/