Son of Hugh Maxwell (d. 1765), 3rd of Dalswinton, and Jane (or Jean) Douglas, a daughter of Helen Erskine and William Douglas, 2nd of Kelhead. Brother of William Maxwell. Married to Ann Handcock, daughter of Peter Handcock of Twyning Manor. They had one son and four daughters before Maxwell's accidental death due to a hunting accident in 1779.
Whilst in the act of loading his gun to shoot small birds, as food for his children's hawk, the gun went off, and the charge having lodged in his face, he was killed on the spot.1 .
Tragically, their eldest son William George Maxwell, a clergyman in the Church of England, also died due to "the accidental discharge of his gun, which rendered necessary the amputation of his arm, under the effects of which he expired."2 On William's death in 1838, Twyning Manor passed to his sister, Helen. She died unmarried in 1858 and was succeeded in Twyning by her niece, Jane Mary Stocker.
Maxwell was a Captain in the 35th foot regiment.
Boswell dined with George William Maxwell and his brother, William, in London on January 1 and July 27, 1763. Boswell and the Maxwells were closely related, the two brothers being grandsons of Boswell's mother's half-sister, Helen.