I'm not sure how TDM comes into this. You would need two computers. Each could have Firewire ports or Thunderbolt ports. Adapters can be used for Thunderbolt to Firewire. Connect the two and boot the target machine into Target Disk Mode. Boot the other normally. Not sure what you think you would do at this point.
Nevertheless, doing a Network Restore will erase the drive, so you needn't worry about overwriting El Capitan. Mountain Lion can be upgraded back to El Capitan. But you would know that had you read what I posted. You would note that re-partitioning the disk drive was the first thing you would do. Perhaps the next time around you could post a much clearer statement of your problem. Then we don't have to guess what you want.
If you have a bootable Recovery HD, then you can do a clean install:
Install or Reinstall OS X from Scratch
Be sure you have backed up your files because the following procedure will remove everything from the hard drive.
Boot to the Recovery HD:
Restart the computer and after the chime press and hold down the COMMAND and R keys until the menu screen appears.
Erase the hard drive:
1. Select Disk Utility from the main menu and click on the Continue button.
2. After DU loads select your startup volume (usually Macintosh HD) from the
left side list. Click on the Erase tab in the DU main window.
3. Set the format type to Mac OS Extended (Journaled.) Optionally, click on
the Security button and set the Zero Data option to one-pass. Click on
the Erase button and wait until the process has completed.
4. Quit DU and return to the main menu.
Reinstall OS X: Select Reinstall OS X and click on the Install button.
Note: You will need an active Internet connection. I suggest using Ethernet if possible
because it is three times faster than wireless.
This should install the version of OS X that you had installed.
If you wish to simply reinstall El Capitan, then do the following:
Reinstall El Capitan Without Erasing the Drive
Make sure you have a current backup before proceeding.
Boot to the Recovery HD:
Restart the computer and after the chime press and hold down the COMMAND and R keys until the menu screen appears.
Repair
When the recovery menu appears select Disk Utility and press the Continue button. After Disk Utility loads select the indented Macintosh HD entry from the the left side list. Click on the First Aid tab in the toolbar.. If Disk Utility reports any errors that have been fixed, then re-run First Aid until no errors are reported. Wait until the operation completes, then quit Disk Utility and return to the main menu. Select Restart from the Apple menu.
Reinstall OS X: Select Reinstall OS X and click on the Continue button.
Note: You will need an active Internet connection. I suggest using Ethernet if possible because it is three times faster than wireless and more reliable.