Have a look at Plink!
It's made by the people who made Putty and its purpose is for exactly what you try to use putty for in your question.
Plink (PuTTY Link) is a command-line connection tool similar to UNIX ssh. It is mostly used for automated operations.
From the Plink Manual:
7.3 Using Plink in batch files and scripts
Once you have set up Plink to be able to log in to a remote server without any interactive prompting (see section 7.2.2), you can use it for lots of scripting and batch purposes. For example, to start a backup on a remote machine, you might use a command like:
plink root@myserver /etc/backups/do-backup.sh
Or perhaps you want to fetch all system log lines relating to a particular web area:
plink mysession grep /~fred/ /var/log/httpd/access.log > fredlog
Any non-interactive command you could usefully run on the server command line, you can run in a batch file using Plink in this way.
Plink Download Link