And how would the vessel slow down?

Precisely DaveB. Sounds like NASA have been on the Turps when they came up with this idea.
What kind of scientific data are they hoping to collect when whizzing past a planet at such high Velocity?? Also the further away a craft gets, the more difficult AIMING the photon gun at it becomes. The craft still needs it's own engines as it will need to do correction burns. Sounds like all the problems a Solar Sail craft would have.

I guess the idea of starting small is the way to go. Sounds a little too easy to pass up.
If you're going to mars, hitting the planet could stop the vessel. Kind of limits the mission however.....

And how would the vessel slow down?

With a similar setup at the destination.

If there is no such system at the destination then it would carry propellant - but only need half as much as usual craft because it get the acceleration "for free" from home. This would still be a very substantial advantage for stuff like missions to Mars

There are lots of questions still to be answered of course, like what happens when a vehicle at near light-speed hits a tiny meteorite.

You could have a portion of the stream directed not at the craft but just to the side to clear the cone of vulnerability.

This is the only viable technology for rapid transport around our solar system and eventually out towards the stars. To that end, the vision must encompass a web of beamers around our system for directed acceleration and braking for a multiplicity of routes. We will weave a transportation web over our solar system made of light. What a wonderful vision that is.

But we are absolutely going to need cheap launches to make it work such that we are lofting tons of equipment into space for deployment of this beamer web. Reusable rockets take us partway towards that goal, but the real cost savers are fully reusable technologies like StarTram and Skylon. We should be building StarTrams right now if we are serious about launching our dreams. With cheap launches we can get heavy equipment onto the Moon and Mars and take serious first steps at establishing permanent presences there.

At least, that's the roadmap as I see it.

This is the only viable technology for rapid transport around our solar system and eventually out towards the stars. To that end, the vision must encompass a web of beamers around our system for directed acceleration and braking for a multiplicity of routes. We will weave a transportation web over our solar system made of light. What a wonderful vision that is.

But we are absolutely going to need cheap launches to make it work such that we are lofting tons of equipment into space for deployment of this beamer web. Reusable rockets take us partway towards that goal, but the real cost savers are fully reusable technologies like StarTram and Skylon. We should be building StarTrams right now if we are serious about launching our dreams. With cheap launches we can get heavy equipment onto the Moon and Mars and take serious first steps at establishing permanent presences there.

A nice vision.
Will take lot of international cooperation. That won't be as pretty and streamlined...

Assuming for one second that the mirrors could confine the photons and produce that much thrust without burning up:
1)The resource "vehicle" would have to be based on the moon to absorb the recoil.
2) The trapped photons would be red shifted more at each bounce due to the relative velocity; eventually passing out of the useful band of the gain medium and probably frying the system as it descends beyond infra red.

I hope this was nothing more than the dream of one of NASA's interns. I'd hate to think they invested more than pocket change on this.

Assuming for one second that the mirrors could confine the photons and produce that much thrust without burning up:
1)The resource "vehicle" would have to be based on the moon to absorb the recoil.
2) The trapped photons would be red shifted more at each bounce due to the relative velocity; eventually passing out of the useful band of the gain medium and probably frying the system as it descends beyond infra red.

You're misunderstanding the technology. Best you read the accompanying paper. Although Bae's idea for amplifying thrust via cavity Q is not infeasible in this context, Lubin specifically states that he has not assumed it for the purposes of calculating performance.

Assuming for one second that the mirrors could confine the photons and produce that much thrust without burning up:
1)The resource "vehicle" would have to be based on the moon to absorb the recoil.
2) The trapped photons would be red shifted more at each bounce due to the relative velocity; eventually passing out of the useful band of the gain medium and probably frying the system as it descends beyond infra red.

You're misunderstanding the technology. Best you read the accompanying paper. Although Bae's idea for amplifying thrust via cavity Q is not infeasible in this context, Lubin specifically states that he has not assumed it for the purposes of calculating performance.
Furthermore, Lubin has been careful when analysing the power capabilities of the reflective surfaces. Indeed, the report allocates several pages to this topic.

The beamer web I described consists of solely a source - not a back-reflecting mirror. Riding that beam is all that's needed.

And with all these laser beams criss crossing interplanetary space not a one ever gets misdirected and fries an inadvertent target? Nobody with a standard drive crosses path's?

An onboard energy source is still a must. It will come, many sources are theoretically possible and need developed.
Until then a light sail would allow slowing down again when approaching a new sun.
A laser boost could get it out of our solar system much more quickly, although the time saved would be small compared to the trip length and cost effectiveness would be nil.

I have yet to have my laser pen launch into space off a mirror.....

If they portrayed this system as a moon-based-laser boosted solar sail, they might have an idea worth exploring.
But their "confined laser beam" without any precision adaptive divergence-compensation for their fibre based laser amplifiers, and a PR video dangling "multiple bounces" as a bonus suggests they haven't a clue.

Conservation of momentum demands back-reaction. Therefore a laser pointer in space, when turned on, will slowly accelerate backwards, in a direction opposite to its beam. With the high power beamer system discussed here, the back-reaction is fierce, and for that reason beamers will be mounted to very sizeable chunks of rock: the Moon, asteroids, etc . To obviate collimation issues, it's a bad idea to try to have one in atmosphere.

This article (original site) is more than 4 months old.
The idea to use photons to propel a spaceship has been around for decades (OST series).
The problem I see is just how big is the power plant?
Reminds me of the time when they made a MHD drive boat using sea water, theory said they would go faster than any craft ever built. True speed was less than 15 mph. I see the same here...

The problem I see is just how big is the power plant?

The power plant is the Sun, via PV.