I have made tabasco-thin sauces with a hand crank food mill. Start with a thin sauce (plenty of liquid). Run it through the mill a few times, each time rinsing out the pulp, skin and seeds from mill screen. After 2-3 runs, you should end up with a consistency like red water. You can then cook it down a bit if you wish to re-thicken.
Food mills are quite versatile. You can make a thicker sauce (but without seeds), but running the liquid through the mill several times but leaving the pulp in the mill. Each pass forces more pulverized pulp through the mill.