It will simply be traveling too fast, and Pluto is simply too small, for the probe to get into orbit.
For them to have arranged for it to slowly catch up with Pluto and get into orbit, I imagine the path would have taken decades if not hundreds of years. (Assuming the fuel capacities we have to work with.)
Looks like they have gone into some detail on a potential mission like this[1], appears that it would take 17 years, at least with this particular launch window Jupiter alignment.
What does it take to get a robotic mission onto a planet (or other solid body)?
1. It's got to be a solid body. That eliminates Jupiter, Saturn, Uranus, and Neptune, straight out.
2. You've got to be able to get there in the first place. Nearer bodies are generally easier to reach, so long as they're not too close to the Sun. It actually took as long to reach Mercury (about 6 years) as it typically does Jupiter, despite the fact that Jupiter is about 10 times further away by distance. Both these and other missions used gravitational assists to reduce fuel requirements, resulting in complex trajectories:
To get to Pluto has taken New Horizons 9.5 years. That included a gravitational asssit from Jupiter. And on arrival, it's going to be trucking along at 49,600 km/h (30,800 mph). That's approaching the speed of the Chelyabinsk meteor (67,000 km/h, or about 41,750 mph).
3. You've got to be able either enter into orbit or slow down once you get to the destination. Gravity assists or aerobraking both help hugely, as they avoid the need to carry fuel, and the tyranny of the rocket equation (more below).
4. You've got to be able to land, softly, on the surface. Again, an atmosphere helps a lot. Or a nearby body and low gravity for a rocket landing (as in the Moon). Pluto's got low gravity, but is so far away we're travelling fast when we get there.
xkcd's Randall Munroe looked at what would be required to catch up with and return the Voyager I probe, similar in spirit to trying to deaccellerate using rockets on arriving at Pluto. It's not pretty: https://what-if.xkcd.com/38/
Slowing down and speeding up are symmetrical, roughly speaking you'd need a rocket similar to the one used to launch New Horizons to put it into orbit around Pluto. So you'd need an enormous rocket to send all of that to Pluto, which is beyond our current technology and budget limits.
