As you blow through the straw, the air rushes out with great speed. So the air goes over the other straw with even greater speed. This leads to a low pressure over the other straw in the water and water rises in this straw. The Rising water hits the air and becomes a mist/spray.
The creation of low pressure due to high speed air is according to Bernoulli’s principle. This is the same principle which says that we should not stand near a fast moving train, as low pressure created there can suck us towards the train and consequences can be extremely dangerous.
You have probably experienced this while driving on the freeway as a truck speeds past you, your car gets pulled in to the truck. Its because the truck created low pressure