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To stop spamming, you can flag the user comments that have exhibited spamming activity. As more and more people flag that spammer, it will show a negative upvote (or downvote). If this keeps happening, that spammer's Reputation Score will go below the normal range of numbers.
The Reputation Score is basically the number in bracket right next to your Steemit username. When dealing with users here, that's a good reflection of how reliable they are, and how engaged that user is with the Steemit community.
You can also leave negative comments calling out the spammer and to request him to stop. As a community, if the bloggers and curators work together, spamming in Steemit can be kept to an absolute minimum. It can be truly eliminated completely because new spammers will continuously join the webstei. But, a healthy community will keep those spammers at bay!