Progressivism did not have as much impact on American foreign policy as one might expect. Two of the three presidents who are seen as progressives did not have particularly progressive foreign policies. The third, Woodrow Wilson, did push much more strongly for progressive ideals in US foreign policy.
Both Theodore Roosevelt and William Taft pursued foreign policies that were not particularly progressive. TR was a staunch supporter of imperialism. He issued the "Roosevelt Corollary to the Monroe Doctrine," claiming the right to intervene in the affairs of Latin American countries whenever the US's interests were affected. His "big stick diplomacy" and Taft's "dollar diplomacy" were aimed solely at increasing US power.
By contrast, Wilson wanted US foreign policy to try to make the world a better, less greedy place. This is in line with the progressives' ideas. This shows up most clearly in Wilson's proposed 14 Points for the end of WWI. Wilson wanted, for example, to create the League of Nations. By doing so, he hoped to keep the strong countries of the world from exploiting the weak.
All in all, progressivism did not have that much impact on US foreign policy until Wilson's presidency.