According to my dictionary, both 混ぜる and かき混ぜる mean "to mix" or "to stir". But what is the difference between the two? Unfortunately, the dictionary does not provide any additional information and I couldn't make out any difference in the example sentences I looked at.
かき混ぜる = to stir
混ぜる = to mix
According to HiNative:
かき混ぜる refers to sticking something hard and stick-like into something else and spinning it around (e.g. using a spoon to mix dough) whereas 混ぜる can be used in a more broad sense which encompasses mixing by other methods as well (e.g. shaking).
混ぜる can be used in all places かき混ぜる is used but not the other way around. Also note that 混ぜる can also have the meaning of "invite me" or "include me" to an outing/event.
You're going to a party tomorrow? Can I come!!!