UPDATE: I have unselected my answer because an icon-less and half-working (see screenshot) version of Photos.app appeared on my system and opened automatically on SD-card insert. This worked and did not cause problems for months, and now Photos is back ?
El Capitan has a new feature called System Integrity Protection. It does not allow the deletion of preinstalled apps. This link gives details for disabling it. The short of it is:
Restart and hold Command+R to go into recovery mode. Open "Terminal", found in the "Utilities menu" and use the commands
$ csrutil disable; reboot
to disable SIP and reboot. Now open Terminal.app normally and do
$ cd /Applications/
$ sudo rm -Rf Photos.app
and live happily ever after.
A few caveats: I don't know what SIP does specifically, but this post suggests you should at least re-enable it right away (and perhaps not disable it at all, ever). Go ahead and do that by using the command
$ csrutil enable; reboot
in Recovery mode (see above). I also don't know whether El Capitan has Photos.app-dependent system processes or not, so your mac may potentially not work the way you want it after this. I have protected myself by first Archiving Photos.app and leaving Photos.app.zip in /Applications/, but again, I don't even know if this is good enough. So proceed at your own peril!
Finally, this will work to get rid of any bundled system app (but the same or more severe warnings apply).
Best Answer
You do not need to disable System Integrity Protection (SIP).
To delete the FaceTime app, do the following:
Backup FaceTime.app via Time Machine or making a Zip archive.
Shutdown your Mac.
Boot to Recovery Mode. Press ⌘R when starting your Mac.
Open Terminal from the Utilities menu.
Run the following compound command adjusting Macintosh HD as necessary if you've modified the default name of the primary startup volume:
After rebooting from Recovery Mode, if you still have the FaceTime icon on the Dock, right-click it and select: Options > Remove from Dock
Note that while this does remove the FaceTime.app, it may/will reappear when macOS is updated/upgraded and will need to be deleted again.
If after having done this and you want to restore the FaceTime app, then restore it using Time Machine, if you backed it up in that manner, or if you created the Zip archive, it would have been created in the /Applications folder, if you moved it elsewhere, move it back and then do the following:
Shutdown your Mac.
Boot to Recovery Mode. Press ⌘R when starting your Mac.
Open Terminal from the Utilities menu.
Run the following compound command adjusting Macintosh HD as necessary if you've modified the default name of the primary startup volume: