I have created a ssh key for my droplet at digital oceans. After few days I have deleted the key from security page and still I am able to ssh using putty with that key. Is it necessary to delete the key from authorized_keys file. If so, then what is the use of adding/deleting ssh keys to droplet on their above mentioned security page?
Hansen is right. Installing keys on Droplets is a one-way deal: they're installed at initial boot only and never updated or removed. That keys repo is used for new droplets only.
To remove a key from a droplet:
sudo nano $HOME/.ssh/authorized_keys
Find and remove that key, and then save. You do not need to restart the SSH process.
If you are trying to manage keys across a team, you need tools like Userify (disclaimer: I work there), SSH.com's Universal Key Manager, or use a tool like Chef or Puppet to actually remove those keys from authorized_keys.