Although it is true - Mean Tweets can be very entertaining, the reality is many things people feel comfortable saying to others online, or allow/excuse because they are funny can be actually be hurtful and create a culture of division online and beyond.
One way to build empathy is to challenge students to apply different tones of voice and delivery to a variety of posts. As a language arts teacher this also allows for an exploration into precision of language - is what you are posting communicating what you want it to?
To accomplish these goals students could collect comments or tweets from the web and put the into a box/bag. Then the students could draw a one out of the bag to read, absent context, in a tone of their choosing.