Why use drilling mud for oil drilling?

It's used to prevent anything coming back up the hole.

Drilling fluids, the circulating fluid for drilling operations, is a mixture of the fluid, the solid and chemical agents. It is usually known as the "mud" or the "blood of drilling" deriving from its distinctive significance.

The main functions of drilling fluids include providing hydrostatic pressure to prevent formation fluids from entering into the well bore, keeping the drill bit cool and clean during drilling, carrying out drill cuttings, and suspending the drill cuttings while drilling is paused and when the drilling assembly is brought in and out of the hole. The drilling fluid used for a particular job is selected to avoid formation damage and to limit corrosion.