The government has ordered all inhabitants to stay indoors, but the meteorological service said the storm was now moving eastwards away from the remote paradise island.
Belal has left thousands of people without power, and numerous cars submerged under floodwaters caused by torrential rains or piled up on streets.
Police said the body of a motorcyclist was found on a flooded highway, the victim of a road accident. Prime Minister Pravind Kumar Jugnauth, in a statement on national television on Monday, confirmed one fatality.
Belal had already battered the French overseas territory of Reunion, leaving one person dead.
The international airport in Mauritius was closed on Monday until further notice and Air Mauritius announced that several flights scheduled for Tuesday, including to France and South Africa, had been cancelled.
- 'Share the anger of Mauritians' -
In his address on Monday, Jugnauth criticised the Mauritius Meteorological Services (MMS) and announced that its director had submitted his resignation.
"I have to admit that the country has had a difficult time because of Cyclone Belal," he said, adding that all decisions made by the government had depended on information from the MMS.
"I am surprised that the arrival of the heavy rains was not anticipated by the weather services. I share the anger of many Mauritians. Those responsible will have to assume their responsibilities."
The government on Monday announced that a curfew would remain in force until noon on Tuesday, with only certain people such as emergency workers allowed to go outdoors.
The Central Electricity Board said 8,400 people in Mauritius, which has a population of almost 1.3 million, were without power.
The MMS said in its update at around 0300 GMT on Tuesday that gusts of up to around 120 kilometres (74 miles) an hour were pummelling the island, a magnet for tourists attracted by its stunning white beaches and crystal-clear waters.
It said cyclone warning 4, the maximum-level, was now in force, but that barometric pressure was rising, "indicating that Belal has already crossed at its closest distance from Mauritius".
"However, the cyclonic winds associated with Belal are still influencing the island," the MMS added.
It warned of sea swells of up to 10 metres (more than 30 feet) beyond the reefs.
"Storm surge will cause coastal inundation along low lying coastal areas. It is strictly advised not to go out at sea and to avoid venturing along beaches."
Severe Tropical Storm Belal is centred at about 150 kilometres (93 miles) south-southeast of Mauritius, and is moving eastwards at a speed of about 15 kilometres an hour, according to agency.
About a dozen storms or cyclones occur each year in the southwest Indian Ocean during the November-April season.
In February last year, Mauritius was lashed by heavy rains and high winds from Cyclone Freddy, which caused a wave of death and destruction in southeastern Africa including Malawi, Mozambique and Madagascar.
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