Yes you can, but it will depend on the power of the drill on how well it will work. Occasional use of a cordless drill for mixing small quantities of paint or materials is generally OK.
But, if you want to mix products on a regular basis you are better off with a corded drill with a more powerful motor. A 450-600 watt motor is the typical output for an everyday DIY drill, but you can get more powerful motors which are better at tackling larger mixing jobs.