The key to this answer is evaporation and the property of evaporation that it causes cooling. The more the surface area the more is the cooling.
A liquid has a larger surface area in a saucer than in a cup. One of the factors affecting evaporation is surface area. Larger the surface area more is the evaporation. Thus, evaporation is faster in a saucer causing more cooling than in a cup. For this reason, we are able to sip hot tea or milk faster from a saucer than a cup.