There's no mixing services that are free, and you must consider the fees before doing your transactions.
With YoMix, they offer a cheaper fees for their services but the mining fees will always depend on the traffic of the network you are going to use.
Be mindful with the minimum though so your transactions will  proceed, as per latest 0.001 BTC is the minimum and if you experience some problem better to communicate right away with their support to address your concern.