Apple has not provided an easy way to recover from this condition. Please read this whole message before doing anything. If you don't feel confident that you can follow the instructions, get someone more experienced to help you. One option is to make a "Genius" appointment at an Apple Store.
This procedure applies only to an iMac or Mac mini with a factory-installed Fusion Drive. If either of the internal drives (an SSD and a hard drive) has been replaced with an aftermarket drive, ask for other instructions.
You'll need to refer to these instructions while no web browser is running, so either print them or load them on another device before you begin.
1. All data on the internal drives will be removed, including Boot Camp data, which is not backed up by Time Machine. You need at least two complete, independent backups. One backup is not enough to be safe. There are ways to back up a computer that isn't fully functional. Ask if you need guidance.
2. Disconnect all external storage devices.
3. You'll need to start up from a Recovery system other than the one on the internal hard drive (if it has one.) There are several ways to do that.
a. If you have a local Time Machine backup (not a network backup), or a compatible installation of OS X on an external drive, then you should be able to start from it by holding down the option key at the startup chime. Select the external drive in the row of icons that appears. By "compatible," I mean an installation that can run on the machine. A version of OS X that is older than the machine is not compatible.
b. If you used Recovery Disk Assistant (or can use it now) to prepare a Recovery system on a USB flash drive, you can start from that by holding down the C key at the chime. No icons will appear. Startup will be much slower than usual.
c. Start up in Internet Recovery mode by holding down the key combination command-option-R at the startup chime. Release the keys when you see a spinning globe. Select a language, if prompted.
Note: You need an always-on Ethernet or Wi-Fi connection to the Internet to use the network features of Recovery. It won’t work with USB or PPPoE modems, or with proxy servers, or with networks that require a certificate for authentication.
4. In the OS X Utilities screen, select Get Help Online. Safari will launch. While in Recovery, you'll have no access to your bookmarks or history, but you won't need them. Load this web page.
5. Triple-click anywhere in the line below to select it:
diskutil cs deleteLVG `diskutil cs list | awk 'NR==3{print $NF}'`
Copy the selected text to the Clipboard by pressing the key combination command-C.
Quit Safari. You'll be returned to the OS X Utilities screen.
6. From the menu bar, select
Utilities ▹ Terminal
The Terminal application will launch. Paste into the Terminal window by pressing the key combination command-V. Wait for a new line ending in a hash sign (#) to appear. If nothing happens, press the return key.
Quit Terminal to be returned to the main screen.
What happens next depends on what version of Recovery you're running.
☞ If the machine came with OS X 10.10 ("Yosemite"), 10.9 ("Mavericks"), or 10.8 ("Mountain Lion"), and you're in Internet Recovery, please take Step 7a and skip Step 7b.
☞ Otherwise, skip Step 7a and go to Step 7b.
If you don't know what version of OS X the machine came with, look it up on this page.
After taking whichever of those steps is applicable, you should have an empty Fusion Drive named "Macintosh HD" on which you can carry out either Step 8a or Step 8b.
7a. Repair the Fusion Drive (see under "Troubleshooting" on the linked page.) Quit Disk Utility.
7b. Enter the command below as in Steps 4-6:
N=Macintosh\ HD; for d in /dev/disk?; do o=`diskutil info $d`; [[ ! "$SSD" ]] && grep -lqw 'APPLE SSD' <<< "$o" && SSD=$d; [[ ! "$HDD" ]] && grep -lqw 'APPLE HDD' <<< "$o" && HDD=$d; [[ "$SSD" && "$HDD" ]] && break; done; diskutil cs create "$N" $SSD $HDD && diskutil cs createLV "$N" jhfs+ "$N" 100%
This is a very long line, and you may not see all of it on the web page. Be sure to select the whole line, not just the part you can see.
Quit Terminal.
8a. If you have a Time Machine backup, connect the backup device and restore your data. If you backed up to a network device such as a Time Capsule, it should be connected automatically.
8b. If you don't have a Time Machine backup, or if you can't restore from the Time Machine backup that you do have, install OS X. Restore the data afterwards in Migration Assistant.
In Internet Recovery mode, you'll be installing the original version of OS X that shipped with the machine. If you've upgraded the OS in the App Store, you'll need to do that again.