Transmission comes as part of the Mint distribution but doesn't get updated with newer features, just security patches. If you want the latest stable version you can add the transmissionbt sources to your system and it will upgrade painlessly via synaptic package manager. The following works for Ubuntu based Mint distributions only, not LMDE.
1. open the page https://launchpad.net/~transmissionbt/+archive/ppa in your browser.
2. click Technical details about this PPA to reveal the code you need to copy and paste.
3. Open Software Sources from the Mint Menu and enter the security password when prompted.
4. Click on the Other Software tab.
5. Click the Add button.
6. Go back to your web browser and next to Display sources.list entries for: change the drop down entry list to lucid.
7. Select the first line of code 'deb http://ppa.launchpad.net/transmissionbt/ppa/ubuntu lucid main' and copy it to the system clipboard.
8. Go back to Software Sources and paste the entire command into the APT line entry box. The click Add Source.
9. Do the same for the second line of code 'deb-src http://ppa.launchpad.net/transmissionbt/ppa/ubuntu lucid main'.
10. Then click Close on Software Sources. The system will download updated repository lists.
11. Open Synaptic Package Manager and click the Reload button.
12. Then from the filter list in the bottom left of the screen click Status.
13. Above that click Installed (Upgradeable).
14. Select the following packages transmission-cli, transmission-common, transmission-gtk (or transmission-qt depending what desktop you use. the right one will be listed), transmission, libevent-2.0-5.
15. Mark theses packages by right clicking them and choosing Mark for Upgrade.
17. Dependencies will be met automatically from Mint/Ubuntu sources so it is safe to proceed as normal and apply changes as prompted.
18. Click the Apply button on the Synaptic Package Manager toolbar.
19. Packages selected will be downloaded and installed on your system.
20. Close Synaptic Package Manager when changes have been applied.