Sakat Bhedan term appears when Dasharath asked a Var from Shani Dev that "he should not do Sakat Bhedan." Sakat means chariot or cart; and Bhedan means piercing right through the middle. Therefore Sakat Bhedan means going right through the middle of the chariot.
Rohinee Nakshatra [Vrishabh 10 to 23:20 degrees] is also known as Sakat or chariot.

Raajaa Dasharath prayed to the planet Saturn not to go through the middle of the Nakshatra Rohinee. The celestial planets move through a 12 degrees wide corridor in the sky. The Saturn seldom passes through the middle of this corridor. Why did Raajaa Dasharath make such a request to Saturn?

Rohinee heralds fertility, agriculture and hence civilization. This is a productive Nakshatra that lays the foundation stone for every kind of growth like the growth of a plant from a seedling. Rohinee is responsible for all kinds of production : Birth, production, origin, propagation, procreation, planting, sowing, sprouting, growing up.

Moon is the Lord of this Nakshatra along with Hast and Shravan Nakshatra. Remember Saturn considers the Moon as an enemy.

Therefore if the Saturn passed through the middle of Rohinee, it will have maximum impact. This impact would adversely affect the birth, production, propagation, procreation, planting, sowing, sprouting, growing up etc. And no king would want that to happen.