That's right: From June 3 to July 2, there'll be a post each day highlighting Teenage Mutant Ninja Turtles canon immigrants. Now, because TMNT canon is a little confusing, it can be hard to tell what counts as a canon immigrant and what doesn't. So for the purposes of this blog, a TMNT canon immigrant is anything (a) from the movies, cartoons, video games, toy lines, or tie-in comic series that later appeared in (b) TMNT volumes 1, 2, or 4 [because they're by the original creators] or TMNT volume 5 [because the original creators are involved, it's the new official continuity, and its goal is to use as much of the diverse TMNT lore as possible].
A note up front - this entry is talking specifically about the team. The individual members all have their own things going on, so they'll each get their own entry. And the IDW team has almost an entirely different roster.
That being said, the team first appeared in Teenage Mutant Ninja Turtles Adventures #19 (April 1991) before being spun-off into their own miniseries, Teenage Mutant Ninja Turtles Present Mighty Mutanimals (May-July 1991). This led to an ongoing series, and then some backup stories in Teenage Mutant Ninja Turtles Adventures. This team consists of Man Ray, Dreadmon, Jagwar, Mondo Gecko, Leatherhead, Wingnut, and Screwloose. Interestingly, Screwloose is the only one that doesn't become a canon immigrant in some way.
In the Mirage continuity, the Mutanimals made a cameo appearance in Tales of the TMNT #58 (May 2009), in a scene showing the multiverse.
In the IDW continuity, Old Hob starts putting together a gang of mutants in Teenage Mutant Ninja Turtles #38 (October 2014). In the next issue, he uses the term "mighty mutant animals". They continue to appear, and eventually get their own miniseries, Teenage Mutant Ninja Turtles: Mutanimals (February-May 2015). This version consists of Old Hob, Herman the Hermit Crab, Pigeon Pete, Mondo Gecko, Slash, Man Ray, Sally Pride, Mutagen Man, and a few others.