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".
White House: Media coverage is 'demoralising'
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The White House has accused liberal media groups of false and irresponsible reporting designed to smear President Trump and the new administration.
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.

TUV Rheinland, which awarded EU safety certificates to the French implant manufacturer, "neglected its duties of vigilance", the court said.
PIP (Poly Implant Prothese) was shut down in March 2010 amidst a worldwide health scare.
The company used sub-standard silicone gel, causing many implants to rupture.
Q&A: Breast implants health scare
Six implant distributors and 1,700 women had sued TUV Rheinland for 50m euros (Â£42m), arguing anything but a cursory inspection would have found problems.
The plaintiffs in the civil case will be given an initial payment of 3,000 euros per victim for surgery to have the implants removed.
Jan Spivey, a British woman who received PIP implants as part of reconstructive surgery following breast cancer in 2002, said she was "delighted" with the ruling.
"Of course TUV has some responsibility and should be held to account. They're the organisation that gives the CE certification for safety, and that was what my surgeon relied on when he gave the implants to me.
"Anybody that gives safety certification for a product that is going to make women very sick does have responsibility," she told the BBC's Newshour programme.
It could open the door to many more compensation claims, says the BBC's Christian Fraser in Paris.
TUV Rheinland had won two previous cases in Germany. This was the first such case in France.
The German firm has said it will appeal against the verdict.
TUV Rheinland awarded PIP - formerly one of the world's leading suppliers of implants - its European safety certificate for 17 years.
The founder of PIP, Jean Claude Mas, is still on trial for aggravated fraud in Marseilles, along with four of his executives.
He revealed during police interviews that he had ordered employees to hide the unauthorised silicone when inspectors visited his factory.
It has since emerged the substandard gel was used in 75% of the implants.
The court heard an employee in charge of quality control had only a cooking diploma - another in charge of the lab had previously trained as a pastry chef, our correspondent says.
A ruling is expected in Jean Claude Mas' case on 10 December.
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.
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A French court has ordered a German company to pay compensation to hundreds of women who were fitted with defective breast implants.