There was no immediate confirmation from North Korea that its troops had begun the demining process, but the South said it expects its neighbor to adhere to the deal.
"In accordance with the military agreement (made during the Pyongyang summit), the removal operation is expected to take place in each other's territories inside the JSA", the Defense Ministry said in a statement.
Military engineers are performing the hazardous task on the South Korean side.
The South's Defense Ministry says it detected North Korean soldiers engaging in what it believes are demining-related work at the two sites.
Teams from both Koreas will flock to Arrow Head Hill in the Gangwon province in South Korea.
It is also closely guarded by tens of thousands of troops on both sides, making it nearly impossible to walk across.
In April, South Korea said it had stopped broadcasting propaganda via loudspeakers along the border to "ease the military tension between the two Koreas".
South Korean President Moon Jae-in has weighed in too, with vague words promoting hope for denuclearization and a better life for the North Korean people.
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"The North is trying to reduce the negotiating value of Washington's potential offer of a peace treaty, by suggesting that "it's not good enough to make us denuclearize", he told South Korea's news agency Yonhap.
"Furthermore, it can never be a bargaining chip for getting the DPRK denuclearized", it said, using the North's full name.
Pungsans are designated a North Korean "natural monument".
Many foreign experts say North Korea are likely running additional secret uranium-enrichment plants.
Critics have anxious that Moon's recent inter-Korean military deals would weaken South Korea's war readiness because the North's nuclear program remains largely intact. Past rapprochement efforts were often stalled after a standoff over the North's nuclear ambitions intensified.
The North entered talks with the United States and South Korea earlier this year, saying it's willing to negotiate away its advancing nuclear arsenal.
South Korea also held a ceremony on Monday marking the recent return of remains of 64 South Korean soldiers missing from the Korean War. They expressed support for the project during talks last month in Pyongyang, the North's capital.
Since fighting during the 1950-1953 Korean War ended in a stalemate, at least nine soldiers have been killed in incidents with North Korean troops, including the killing in 1976 of two USA soldiers.