When I initially created the droplet with Ubuntu 14.04, I added the MongoDB 3.0 as the one-click application. However I later decided to install the LAMP stack manually. Since I don't need it or rather have no use for it, I would like to remove the MongoDB instance associated with my droplet.
You could "rebuild" your droplet from the base Ubuntu 14.04 or LAMP images, but you would then lose any modifications that you've done.
The MongoDB image itself is fairly simple. It just provides MongoDB pre-installed on top of the Ubuntu base image. To completely remove it and the repository providing it, you can run:
sudo apt-get remove --purge mongodb-org
sudo apt-get autoremove
sudo rm /etc/apt/sources.list.d/mongodb.list