It depicts a cartoon figure of Trump with a bloodied knife in one hand and the statue's head, dripping with blood, in the other. It carries the caption: "America First".
The artist who designed the cover, Edel Rodriguez, a Cuban who came to the United States in 1980 as a political refugee, told The Washington Post: "It's a beheading of democracy, a beheading of a sacred symbol."
The cover set off a debate on Twitter and in German and international media, with Alexander Graf Lambsdorff, a member of Germany's Free Democrats (FDP) and vice president of the European Parliament, describing it as "tasteless".
The cover follows a series of attacks on Berlin's policies by Trump and his aides, marking a rapid deterioration in German relations with the United States. Chancellor Angela Merkel was the go-to European ally for former U.S. president Barack Obama, who praised her as "an outstanding partner".
Last month, Trump said Merkel had made a "catastrophic mistake" with her open-door migration policy, and this week his top trade adviser said Germany was using a "grossly undervalued" euro to gain advantage over the United States and its European partners.
No one was available for comment on the Spiegel cover at the U.S. embassy in Berlin.
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