There is no TTL functionality currently in Titan. An issue has been opened regarding this feature request:
https://github.com/thinkaurelius/titan/issues/523
Please consider adding your support for and comments on this feature to the issue.
This question comes up on the mailing list with some frequency. The most recent one can be found here with an offered best solution for doing this now. In summary, the idea is to create a timestamp property on vertices (or edges for that matter) then use Faunus to clean up expired graph elements.