Generally the gravity assists act on other planets on the way to the destination. For example, Cassini got assists off of Venus twice, then Earth, then Jupiter on its way to Saturn.

Note: I'm no astrophysicist, and this is just back of the napkin math

Uranus is the physically closest planet to Pluto at the minimum distance of 11AU (about 1,64 billion km). Pluto's escape velocity is about 1,2 km/s (putting the orbital velocity at about 0,7 km/s). So a naive brake on Uranus would need to put the craft such that it brakes down to less than 1 km/s. 1,65 billion km at 1 km/s is about 52 years. Which seems to be a like letting off the gas in a car while going up a hill to break, but then getting to the top and still needing to go 50 miles to your destination. So something else needs to be in place other than just relying on gravity assists/braking.