Is there any way to save the PuTTY output to a file using the command line? I know this is easily done using the GUI but in my case it has to be done automatically.
The specific program putty is not designed for this. Instead use plink, a different program in the PuTTY suite,
which uses the same session settings and keys as putty but gets input from stdin and puts output to stdout,
both of which can be redirected in the usual ways. See http://the.earth.li/~sgtatham/putty/0.63/htmldoc/Chapter7.html#plink .