Generally speaking, no. Because granite is very dense, and not very porous, its ability to absorb liquids that cause stains is highly reduced.
Granite is approximately 95 to 98 percent stain resistant, and is virtually maintenance-free. This is why it is the stone material of choice for outdoor projects such as patios, courtyards, driveways, footpaths and steps.
If by chance there is a stain, it can usually be removed using a poultice or paste that will draw out the oil from the stone.