It will be necessary to wash your stable floor mats from time to time.
You can use a bucket of diluted disinfectant (if it’s safe for your horse then it’s safe for the mats) and a broom.
Don’t use products containing bleach or abrasives.
​Wash the top surface of the mats.
If you feel it’s necessary to lift the mats to clean underneath always mark the mats and corresponding edges to ensure that they are put back in the same order.  
Do not leave mats to dry in strong sunlight or leant against a wall for a long period of time as they can distort.
Try not to lift and wash the mats too often as the locks tighten up with use and lifting upsets this process.
If the mats are dry and clean underneath then they don’t need lifting.
A powerful multi-purpose outdoor cleaner like Jeyes Fluid* is great stuff, just dilute it down a bit before use. It's anti-bacterial and anti-fungal so it's perfect to clean your stable with.
*Other cleaning products are available.