Yes, it's possible. Register two different usernames with two different email addresses and register the blogs separately under each so they aren't associated.
However, if you have the blogs registered under the same username now then read on. When we register a username account here the email address we provide becomes our unique identifier. When we are logged into WordPress.com and register a blog it's registered to that username account we are logged in under and to the email address which is our unique identifier. We can register as many blogs as we wish and provided we are using the same username account then all the blogs will be registered under it and the associated email account. We can change our "display name" but that display name will appear on all blogs registered under the same username account.
In order to completely separate the blogs that you do not want to be associated with each other you register another username account using a different email address when you are logged out of WordPress.com. http://en.support.wordpress.com/register-a-blog/