From La Guardia you can probably take a flight to one of the hubs of American airlines (Dallas, Miami, Chicago or Atlanta) and from there by one of them to Mexico. Actually there are many ways to get to Mexico from La Guardia, but I advise you to leave from JFK that has direct flights.
There are several airlines that will take you directly. But I don't think you can go from this airport.
Not direct. Only with scale.
This airport does not make international flights.
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