While you're in the Mentions center, you'll find The Delete button under each mention. You can use it to delete just that specific mention or delete and block its source, preventing your project from collecting more mentions from that domain/social media author.
You can do that for individual mention:
Or you can delete more mentions by ticking the box in the bottom right corner of the mentions you want to get rid of from your dashboard:
And then scroll down to the end of the mention stream to find your Global settings. Hit Delete and confirm your decision when asked to do so.
You can learn how to delete particular mention by watching this quick tutorial: