Are Taurus Gemini Cusps compatible with Scorpio Sagittarius Cusps?

(1) Nothing is fixed at all sign to sign, and (2) these are just the Sun signs.

1. Astrologically, the strength of attraction is strongly influenced by several factors, including especially the positions of Venus, Mars, Moon and the Moon's Nodes, as well as the Sun. On top of this, other planets can activate points that make very strong connections (either positive or negative) and bring their own touches -- for example, Uranus can bring in a frisson of differentness, Pluto a bit of obsession, or Neptune some elements of idealization. Astrologers compare two charts to see how the elements in them connect, and relationships even have their own separate charts, based on a composite of the two individuals involved. You really need to have the whole birthchart to see, and that's something that is very individual. (See astro.com for a free service to get your birthchart. For a complete horoscope you need to have the date, time and place of birth, but even the just the date will give you a lot more idea of how two people's charts fit together.)

2. All that said, in theory Taurus/Gemini and Sagittarius/Capricorn cusps indicate Suns that are 150º apart, which is viewed as having not so much in common. To some extent though, that will depend on which elements predominate -- Taurus and Capricorn are very compatible, and so are Gemini and Sagittarius, but Gemini and Capricorn don't have much in common, and nor do Taurus and Sagittarius. But don't base anything, and definitely not any decisions, on just the Sun signs.