In short, no. Elites, or groups later identified as elites, have existed but the execution of what might be called extra-ordinary or special operations were carried out by ordinary soldiers with no particular training that might make them a 'special force'.

For example, knights certainly considered themselves (and have come to be perceived as) elite warriors of the Central and Later Middle Ages. But their training was for ultimately generic warfare and to able to ride a horse and hold a spear straight while doing so. They weren't purely one trick ponies, excuse the pun, but to describe this as a spec. ops force would be wildly anachronistic.

/u/OldWorldGlory helpfully collated a number of responses which explain this further and provides others which might be what you were looking for - what were some Ancient or Classical military elites. The search function (using either 'elite' or 'special force') should provide you with any more recent questions.