How can I delete collected mentions?

You can learn how to delete particular mention by watching this quick tutorial:

The Delete button is located below each mention. You can use it to delete just that specific mention or delete it and block its source, preventing your project from collecting any more mentions from that domain/social media author. 

You can do that for individual mentions:

You can also mass delete mentions via group actions. To do this, tick the box in the bottom right corner of the mention(s) you want to delete:

...And 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 also delete mentions from a given domain or containing a given word by filtering your results and deleting them via global settings.

First enter your domain name in Filter by domain and click Search.

Once you do that, mark all the mentions you want to delete - the easiest way to do this is scrolling to the bottom of the page, hitting Select all, and then Delete.

If you want to delete mentions containing a given word, enter the word in the internal search box:

...and scroll down to the bottom of the page, hit  Select all and Delete.