The Miiverse clone is called "Xboxverse". In Japanese, it's called "Hakoverse" (箱バース), with "hako" (箱) meaning "box" and being one of the console's nicknames in Japan. To be clear, this isn't a Microsoft Japan joint, but rather, the work of Japan's fledgling Xbox 360 owners. In Japan, the Xbox 360 hasn't exactly lit the country on fire since it never sold well.
The Xboxverse is browser-based and obviously not part of Xbox Live. Community members, however, are uploading Miiverse-style drawings—as well as drawings that would most likely be clamped down on pretty quick in the Miiverse.
Also ironically infected with NSFW drawings as the Miiverse at times, for example Ubisoft's The Adventures of Tintin, that game's community is filled with NSFW drawings if you know, it's tintin in Japan after all.
This is a pretty interenting feature of Xbox Japan that I thought it would be nice to use as well.
Source: http://xbox.verse.jp/index.php