There's a couple of ways to mix your coins.
Obviously, there are bitcoin mixing sites. bitmixer.io is the most known one, but there are others such as cryptomixer.io.
Another way of mixing your coins is to buy altcoins with the bitcoins you want to mix (preferably one that is stable), send it to another exchange, then exchange it back into bitcoin and sending them to where ever you want.
Yes, and by using this way of mixing with exchanges you should have more security.
Of course someday an anonymous mixing site owner will disappear with the coins.
If you use a known exchange you should be saver.