Which could include a review of underperforming assets such as its South African platinum arm, and restructuring the company?
Analysts overwhelmingly believe he can, and their enthusiasm was reflected in market results on January 8, when his appointment was announced.
Anglo American closed 1.57% higher than its R278.50 opening, but AngloGold Ashanti closed down 2.83% on its R251 opening price following the news that Cutifani would be stepping down as chief executive.
The majority of analysts consider Cutifani, who left AngloGold to take over as chief executive of Anglo American on April 3, the strongest contender to replace outgoing chief executive Cynthia Carroll.
It was no secret that the job is considered one of the toughest in the mining business because of its deep and difficult mines and Cutifani, with his experience in South Africa and mining experience in six countries, is seen as the man for the job.
Shares in Anglo American have underperformed the sector by almost 20% since the start of last year. They lost $14-billion in value, driven largely by violent strikes in South Africa, delays and cost overruns, low demand for platinum, escalating costs at the group's Brazilian flagship iron ore project, Minas Rio, and operational problems at its Chilean copper project.
Cutifani will spend his first two months in the post taking part in a review of Anglo American.
Analysts described Cutifani as amiable and a person who is very good at building relationships, which could be why his appointment received the nod from the National Union of Mineworkers and shareholder Public Investment Corporation, although both organisations had indicated they would like to have seen a black South African heading the group.
The 54-year-old former Australian coal miner and father of seven, who has South African residency, was appointed in November last year as president of the South African Chamber of Mines. Speaking just two days after his appointment, he took a conciliatory stance on the industrial action that followed the strike at Marikana mine.
Recognising the socioeconomic factors that had contributed to the strikes, which started in September, Cutifani appealed to mining companies to get involved and to become "part of those communities in every sense of the word".
In terms of the Mining Charter, the companies are required to work on social and labour plans to assist surrounding communities. Cutifani called on companies to ensure that all workers are "treated with dignity and respect".
He also earned the respect of the government by greatly reducing mining fatalities at AngloGold during his tenure.
Cutifani's affection for South Africa, where he has lived for five years, is seen as unlikely to prevent him from splitting off assets from the group's South African operations.
Mining experts believe that the restructuring of Anglo American's battered platinum arm, Anglo Platinum, which is expected to result in job losses in that sector, is something he will not shy away from.
He closed AngloGold mines during the recent strikes and reduced dividends to protect the company.
"Mark (Cutifani) is a pragmatic guy. At the end of the day he will do what is good for the business and what shareholders want," said one analyst.
Anglo American's review of the sector is expected to be announced at the end of January, ahead of the group's results the following month.
At AngloGold Ashanti, Cutifani turned around a struggling company in a relatively short time.
His decision to increase the company's exposure to the spot gold price by winding down a loss-making hedge book was widely praised as having saved the company millions. A strengthened gold price worked in his favour and assisted his performance.
Analysts say Cutifani never excluded a spin-off of AngloGold from Anglo American when he headed that company, which is why most feel he will not shy away from that decision now, should it be deemed necessary.
One analyst expressed concern that Cutifani's past management shows a flare for operation management, rather than new deals and restructuring, which Anglo American needs.
This was countered by analysts who believe Cutifani has proved himself as head of AngloGold and that, as a mining engineer and someone with years of experience in various areas of mining, "he knows how to build an asset because he knows what the going price should be".