I don't know if this answer fits the sub's rules, but Saavedra is a Spanish surname, as you can quickly check in the Spanish National Institute for Statistics (simply search by "apellido"). Here you can see more people named Saavedra.

So the reason Cervantes had Saavedra as his second surname is in no way connected to Sanskrit.

The name Saavedra (or Sayavedra that is most likely a different spelling of the same name) has been used in Spain since medieval times, and Miguel de Cervantes not only adopted it himself but also gave it to several characters in his books. It was most likely not accidental given the circumstances.

Although Miguel de Cervantes adopted the name Saavedra arbitrarily, he was related to the member of this family, namely to his distant cousin, Gonzalo Cervantes Saavedra who also pursued literary career and had to leave his native Cordoba in 1568 after he got engaged in a duel with a prominent noble. Miguel could have related to his cousin, as the same kind of trouble forced author of 'Don Quixote' to leave Madrid a year later. After leaving Cordoba, Gonzalo entered the service of the famous Don Juan of Austria, possibly fighting at Lepanto and later traveled to West Indies in 1594 where he presumably perished in a storm when the ship carrying him sank near the coast of what is now Cuba. Thus, one can say that Gonzalo was quite close to the ideal of an 'adventurer', especially by the standards of the era and an embodiment of the virtues of fictional characters such as Ariosto's 'Orlando Furioso'.

It is not exactly known when de Cervantes adopted new name and whether he did it before giving it to several characters of his creation, most notably the protagonists of 'El trato de Argel' and 'El gallardo español', although it is speculated that he might have started using the Saavedra name in the captivity, i.e. between 1575 and 1580, before he wrote either of the aforementioned pieces.

According to María Soledad Carrasco Urgoiti, the name Saavedra has been chosen by Cervantes on purpose. She notices, that the Saavedras were quite renowned family that embodied the spirit of the Spanish-Moorish frontier. This family quite likely originated from Galicia, then settled in Seville around 1350 and in the course of the next hundred years they rose to the prominence as one of the most influential families in the city. They were renowned both for the military endeavors in the fights for Granada and for their mercantile acumen, dealing with both Spaniards and the Moors. Carrasco posits, that history of the Saavedras could have been appealing for Cervantes both as a fitting name for tragic heroes and, to some extent also for himself, especially after his captivity and hardships he endured in the North Africa.

On a final note, Miguel de Cervantes was not the only writer who adopted this last names, as the same did his contemporary Juan José Martí (1570-1604) who has chosen 'Mateo Luján de Sayavedra' as his nom de plume several years before his death.

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Garces, M.A., 'Los Avatares de nombre: Saavedra and Cervantes' ['Avatars of the name: Saavedra and Cervantes'] in: Revista de literatura, LXV, 130 (2003), pp. 351-374.

Carrasco Urgoiti, M.S., 'El gallardo español como héroe fronterizo' [Spanish gallardo as a frontier hero]. Articles from the Third International Congress of Cervantists. University of the Baleares, Palma, 1998, pp. 571-81