Mastodon is a decentralized social platform, meaning that its thousands individual communities exist on separate servers, but they all exist under one network. In response to Tumblr, Mastodon created a post with reasons to choose its platform as your new social media site.
"It's a completely decentralised social network which combines the best bits of Twitter and Tumblr, but the technology is structured in a way whereby it can never be shut down," a post advocating the switch to Mastodon says.
For more alternatives, a Tumblr user has created a master list of websites that could be potential options.