Some German newspapers criticised the cartoon, while the German vice-president of the European Parliament called it "tasteless".
The cartoonist, Edel Rodriguez, said the image represented "the beheading of democracy".
US-German relations have deteriorated under President Trump, who has criticised the policies of German Chancellor Angela Merkel.
He said last month that her policy of welcoming masses of migrants who arrived in Germany had been a "catastrophic mistake". His trade adviser also recently attacked Germany for gaining unfair trade advantages from a "grossly undervalued" euro.
The front cover image is similar to one that appeared on the front page of the New York Daily News in December 2015, also showing Mr Trump beheading the Statue of Liberty but in a less gory fashion.
Mr Rodriguez, who arrived in the US as a political refugee from Cuba in 1980 told the Washington Post that he wanted to make a comparison between the Islamic State and Donald Trump, saying "both sides are extremists".
Der Spiegel editor Klaus Brinkbaumer wrote in an editorial that Mr Trump was "attempting a coup from the top" and wanted to "establish an illiberal democracy".
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Alexander Graf Lambsdorff, a member of the Germany's Free Democrats and vice-president of the European Parliament, said the cover said more about Der Spiegel journalists than Mr Trump.
"The cover plays on the lives of terror victims in a very nasty way," he told Bild.
Several other magazines are using the front covers of their next editions to comment on the US president and his policies.
Bloomberg Businessweek shows Mr Trump holding an executive order, which says: "(Insert hastily drafted, legally dubious, economically destabilizing executive order here)."
British weekly The Economist, which has endorsed both Republican and Democratic presidents, pictures President Trump throwing a molotov cocktail.
The New Yorker, a liberal magazine which endorsed Hillary Clinton, shows the Statue of Liberty's flame extinguished.
The conservative National Review's cover story defends nationalism, which it says critics of Mr Trump's inauguration speech wrongly see as dangerous.
Germany's influential weekly news magazine Der Spiegel has come under fire for a cover image showing US President Donald Trump beheading the Statue of Liberty.