U.S. backing for the PKK/PYD is a major point of contention between Ankara and Washington.
"Brett McGurk is definitely giving clear support to the PKK and YPG," Cavusoglu said, referring to the Syrian group by an alternative acronym.
"It will be beneficial if this person is replaced."
McGurk was appointed as a presidential envoy for the anti-Daesh coalition by ex-President Barack Obama in October 2015.
Three months later, he was pictured alongside PKK/PYD militants in northern Syria, angering the Turkish government, which has labelled the group a terrorist organization closely affiliated to the PKK.
The PKK has waged war against Turkey for more than 30 years and is also listed as a terrorist group by the U.S. and EU.
However, the U.S. views the PKK/PYD as its main ally in Syria and earlier this month President Donald Trump pledged to arm the group ahead of the planned attack on Raqqah, Daesh's remaining Syrian stronghold.
Cavusoglu's comments in an interview with broadcaster NTV, came after he returned with President Recep Tayyip Erdogan from a visit to Washington.
He said Turkey had told the Trump administration that Obama-era officials could damage relations between the countries.
The minister described Trump's government as "more sincere than the previous one" and said Turkey had secured promises that the weapons given to the PKK/PYD would not be used against Turkey and that the U.S. would respect Syria's territorial integrity.
"We told them that the YPG participates in the Raqqah operation not to liberate the city from Daesh but with the aim of declaring an independent state in the future," Cavusoglu said.
U.S. officials had not objected when told that Turkey could attack the PKK/PYD, as it did in airstrikes last month, he added.
He also commented on recent tensions with Germany over Turkey's refusal to allow German lawmakers to visit their troops stationed at Incirlik air base in southern Turkey -- the main site for launching airstrikes against Daesh in Syria.
German Foreign Minister Sigmar Gabriel said Wednesday that Germany would consider moving its forces out of Turkey if the stand-off persisted.
"If Germany decides to withdraw from Incirlik, it is their decision," Cavusoglu said.
"We will not beg. They wanted to come and we helped them. If they want to leave, we will say 'Goodbye'."
Since 2015, Germany has stationed six Tornado surveillance jets and a tanker aircraft at Incirlik, along with around 240 personnel.
Asked if Erdogan and German Chancellor Angela Merkel would meet at May 25 NATO summit in Brussels, Cavusoglu said there was no demand for such a meeting from Merkel yet.
"If there is, we will surely meet. We prefer to solve problems through dialogue," he added.
In his interview, Cavusoglu also commented on Ankara's extradition request for U.S.-based Fetullah Gulen, considered by the Turkish government the mastermind of July 15 failed coup.
"We told them [US officials] that some measures including provisional arrest needed to be taken. Trump said they were taking this matter very seriously," he said.
Cavusoglu also noted that together with U.S. Secretary of State Rex Tillerson, he was assigned to coordinate all works and efforts in this regard.
According to the Turkish government, the Fetullah Terrorist Organization (FETO) led by Gulen orchestrated last year's coup attempt which left 249 people martyred and nearly 2,200 injured.