Apple - How to install OS X 10.9 on a new Mac mini loaded with OS X 10.11

You probably can not do this. The older versions of the Apple OS X operating systems are not capable of running on hardware yet to be designed. For this to work, Apple would have to have released an updated version of OS X 10.9, which they have not done. Therefore, OS X 10.9 will not be able to recognize your newer machine's hardware.

PS: Apple has a support article for this as well, see Use the version of OS X that came with your Mac, or a compatible newer version.

Assuming that you're talking about the latest Mac mini (Late 2014) at the time of writing, you won't be able to install 10.9 on it. It shipped originally with 10.10, so that'll be the earliest that you can install on it in any officially supported way.

It's important to note that when installing supported older versions of Mac OS X on a Mac, you can use the standard installers for all versions except for the original OS version that the model shipped with. To install this version, you should use the Internet Recovery based installer (or for older models, the recovery discs that came with your Mac).

Here be dragons...

If a machine is sufficiently similar to a previous generation and has enough driver support, it might be technically possible to get a prior version of OS X to boot on it, but it's almost certainly going to require manual tweaking to bypass the system identifier checks that happen. It's a totally unsupported thing to do and very likely to be unstable. You're almost in Hackintosh territory here.

If you really want to try this, borrow a friend's older Mac and make an installation of 10.9 to an external drive and try booting it on your Mac mini (holding down the option key at boot to boot from the external drive). If it doesn't boot, try booting it into safe mode. If that doesn't get you any further, try verbose or single user mode, which can give you hints as to what's stopping it booting and what you might have to tweak.

Note: If you're booting from an external hard drive, you'll have to be quick to press the keyboard shortcuts to trigger these different boot modes after you hit the return to boot the Volume.

Why do this?

It's common for Mac developers to need to do this. If you're developing software for the Mac and you're supporting anything older than the latest version of Mac OS X, you should be testing your app on all OS versions that it's supported on.

For example, I've got a 13-inch MacBook Pro (Early 2011) that has partitions (~35 GiB each) for every Mac OS X version from 10.6 onwards that I keep up-to-date with system updates, plus extra partitions for the beta releases of the current stable Mac OS X release and the beta releases of the upcoming Mac OS X release. Keeping an old machine around (at a frugal spec) for this purpose is also a good for QA because it ensures that you're also maintaining acceptable app performance on slow old hardware that your customers might be using (I've also keep a 2008 MacBook Pro and PPC Mac mini for this purpose).