Can cops kick you out of a public place?

Legally speaking it depends on the details of what kind of public place and what you were doing there.

Unless the location is truly a government-owned location (e.g.: park, street, sidewalk, etc - clearly a "public" place) -- businesses which invite people to come and visit and/or do business (e.g.: stores, shopping malls private parking lots, etc) are not truly "public" places as in the first example. They are best described as "places to which the public is invited," and are, in fact, private property.

The owners/managers of this private property CAN control who they wish to remain there and if you refuse to leave at their request they can have the police take action to remove you.

In practice however, the answer boils down to "yes," the police CAN do so.

Attempting to stand on what you perceive to be your legal rights (which may or may not really exist... depending on the details) could result in your being arrested and charged with something such as 'trespass.' In many cases the status offense, of "Disorderly Conduct" suffices as a charge (i.e.: If you aren't acting in an "orderly" manner, then you're disorderly)