He studied at the Latin school in his birthplace Gouda under Jacobus Hovius and at the University of Leiden. After his studies he made the usual "grand tour" of a Dutch gentleman to France. He married Johanna le Gillon on April 4, 1655, a marriage that was to remain childless .
Beverningh was coopted in the Gouda vroedschap and elected schepen in 1645. The very next year he was sent as a deputy to the States of Holland. In 1651 he represented the province of Holland in the Groote Vergadering (the "Great Assembly", a kind of constitutional assembly) of that year, which inaugurated the First Stadtholderless Period in the Republic. In 1653 (the year in which Johan de Witt became Grand Pensionary) Beverningh was made a member of the Holland delegation in the States-General of the Netherlands. De Witt and he were to become close associates.
Cromwell and Beverningh agreed to a secret annex to the draft treaty, that would become known as the Act of Seclusion. This Act was to be solely signed and ratified by the States of Holland, without the knowledge of the other Dutch provinces. It contained the solemn undertaking of the States of Holland that they would never appoint William stadtholder in their province, and would bar his appointment to high federal office in the Republic. After the States General ratified the treaty, without the secret annex, the States of Holland convened in secret session a few days later to discuss the secret annex. It was ratified over the objection of five Orangist cities by the States, and the instrument of ratification was sent to Beverningh in London, however with the instruction not to hand it over, unless it was absolutely necessary.
Meanwhile, the clerk of De Witt, Jan van Messem, betrayed the secret existence of the Act to the stadtholder of Friesland, William's kinsman Willem Frederik of Nassau-Dietz. The Frisian States now demanded an inquiry in the States General into the conduct of Beverningh and the other negotiators. The States-General instructed the negotiators to hand over their papers, including the instrument of ratification unless that no longer was in their possession. De Witt, always a master of the legalistic phrase, was the author of this clause. He also persuaded the States-General to send the instruction in cipher, under a letter in plaintext in his own hand, warning Beverningh of what was afoot. Thus forewarned Beverningh immediately handed over the instrument of ratification to Cromwell, while the instructions were still laboriously being deciphered by the Dutch delegation. He therewith confronted the States-General with a fait accompli.
The resulting scandal was eventually laid to rest, but the States of Friesland blocked Beverningh's appointment as thesaurier-generaal (Treasurer) of the Union, that was first proposed by Holland in 1654, until 1657 (during which time the function was formally left vacant).
Meanwhile, he was appointed schout and later burgemeester of his native city. He acted as gedeputeerde-te-velde (a kind of political commissar) at the headquarters of William III in the campaign against the French during the Year of Disaster, 1672. After the popular revolution that brought William to power as stadtholder, and brought about the fall of the De Witt regime, Beverningh quickly changed sides from the States party (of which he had been a prominent exponent) and joined the new regime. He was one of the Gouda regents who welcomed the new stadtholder at a festive banquet in the city.
Beverningh also acted as a maecenas, enabling the Dutch botanist Paul Herman to travel to the East Indies, a journey that resulted in his Paradisus Batavus (1698), a standard work about orchids. He helped finance the purchase of the library of Isaac Vossius for the Leiden University Library.
While helping to catalog this library, Beverningh fell ill (possibly after he fell off a stepladder). He died at his estate after a short illness in October, 1690. He was buried in the tomb he had bought in 1668 from the Blois-van-Treslong family, in the St. Jan's church of Gouda.