Alexander Asboth was born on December 18, 1811 in Keszthely, Zala, Hungary to János and Anna Mária (Tátray) Asbóth.
When Asboth was eight, his family moved to Sombor, Serbia. He wanted to become a soldier like his elder brother Lajos, but his parents wanted him to become an engineer.
Asboth studied at the Mining Academy of Selmecbánya and the Institutum Geometricum in Pest. He then trained at the Hungarian military academy.
He served in the Austrian army, and was engaged later in engineering and in the law. In the great Hungarian insurrection of 1848-1849 he fought under Kossuth, shared with him his exile and internment, and accompanied him to the United States.
Like many other central European revolutionary exiles, he became an American citizen, and at the beginning of the Civil War he was appointed an officer by reason of his military experience. In the autumn of 1861 he was on the staff of Gen. Frémont, and in the following winter he commanded a division under Gen. Curtis in the campaign along the borders of Missouri and Arkansas. He was wounded at the battle of Pea Ridge, March 1862, and despite his wound was in action the next day at the head of his division.
The same month he was commissioned brigadier-general of volunteers. After this he was in command at Columbus, Kentucky, and at Fort Pickens, Florida. At Marianna in Florida in 1864 he was severely wounded in the arm and in the cheek-bone, and from the effects of these wounds he never recovered.
He left the army, with the brevet of major-general, in 1865, and was appointed United States minister to Uruguay and Argentina, dying at Buenos Ayres not long after his arrival.
Asboth was never married.
