There isn't any way to disambiguate one use of the word with the other one; it all depends from the context.
In your case, since you are watching a photo, that helps: If you are looking a photo showing a town, then È questo il tuo paese? would be understood as "Is this your town?" not as "Is this your country?"
If, differently, you were watching the map of a country showing the full country, then È questo il tuo paese? would be understood as "Is this your country?" if you are not pointing at a specific town shown on the map (e.g. the capital of that country).
In other cases, there are set phrases for which the meaning is not ambiguous: In un Paese democratico, paese would be understood to mean country, not town; that is also true for essere al servizio del paese, Paese nemico, or il paese quest'anno voterà due volte. While paese is often written capitalized, it can still mean country even when it is not capitalized.
As side note, paese has also a third meaning: vast territory, generally inhabited and cultivated.