Playframework 2/Specs2 does not keep state between tests unless you keep state in your test classes, your application or any external place you keep data.
If for example your application would save a user to a database in one test and test for the existance of that user in another test then of course that would make your test interfere with each other.
So I guess you need to figure out some way to clean out the database where you keep your data between each test.