There is a zero percent chance. They are completely separate groups, from different times and different geographies. They spoke languages in separate groups, albeit both Indo-European (the Saxons were a Germanic people, while the Scythians were in the Indo-Iranian group, with a lot of mixture with Samartian, Siberian groups, Khotanese, etc.) Their material cultures were completely separate.

That their names vaguely sound similar is just a coincidence. The typical ancient terms for Scythians are Σκύθης (Greek), Skudra, Sug(u)da. All of these come from the Proto-Indo-European root **(s)kewd-*, meaning "shoot." Their name for themselves seems to have been skuda, "archer," which fits with their preferred style of fighting. The word Saka for them is from Old Persian root *sak- "go, roam," probably meaning "nomad." The Saka were technically distinct from Scythians, being Iranian/"Persian" by language and culture.

The origin of the name "Saxon" is unknown, but most think it relates to a type of knife weapon, the seax in Old English (sax in German and Old Norse). There are multiple spellings and terms for the "Saxons" in Roman sources, with Saxōnēs being the most accepted.