Does teleportation negate/remove momentum?

What kind of teleportation are you thinking of? If it's like a time travel idea using wormholes, some of those theories boil down to tunnels, basically. Off the top of my head, I'd say momentum would remain, then...

I'd say it's up to you to define what happens. Since the idea of your teleportation drive is contrary to the natural laws of physics anyway, what happens during or immediately after it would be whatever you say happens.

If you want to justify maintaining momentum, you could rationalize that since momentum is mass times velocity, and the laws of physics say that mass/energy can't be created or destroyed (but can be interconverted), that the momentum after emerging must be equal to the momentum when it entered.

Or, just say what happens like you're the authority, which in this case, since it's your story, you are.

Good luck.

Presuming teleportation exists, I'd say yes, momentum, speed, energy, all those are conserved, meaning yes, if it's flying fast before it's teleported, it'll be flying the same speed and direction after it's teleported.

Larry Niven wrote several stort (or less-than-novel-length) stories involving on-earth teleportation, and in one (sorry, no idea of the title offhand) he describes a large mass in the middle of a pond that moves back and forth at random intervals. It takes up the difference in momentum from someone transporting from one part of the Earth to another. For a simple example. if you transport from one point on the equator to the point 180 degrees away, you would be moving opposite the direction of the Earth's spin on the destination site (because that's the direction you were moving - WITH the Earth's surface at the source site). The teleportation system corrects your momentum/speed so you're going at the same speed as the destination. The difference in momentum is put into the mass in the pond.

You'd also be upside down at the destination, and the teleporter presumably turns you 180 degrees so your feet are still on the Earth side of your body, instead of you ending up on your head.

Between points in space (zero gee), all this rearrangement would presumably not be necessary.

I would say, if you do the whole "molecular scan, energy beam, molecular reconstruction" type of teleportation, momentum would not be conserved between points.

Also, it's not moving relative to the spaceship or its teleportation device, so wouldn't it stand still from that point of view?

It's up to you but I'd think that some of the energy of momentum would get used up in the teleportation. Even if you want to have momentum maintained or completely lost, if teleportation of space objects exists, dropping asteroids on a planet would still be an effective weaponization of the technology. A big enough asteroid simply falling into the planet's gravity would cause devastating damage.

since energy can't be created or destroyed, then it should keep moving.

Unless your teleportation drive uses its kinetic energy to work.

Teleportation violates conservation of energy anyway, so whether it conserves momentum is up to imagination.

What if all movement in the world itself is a function of teleportation: For any moving object, its new xyz position in the universe is accomplished by the rapid and repeated destruction and re-creation of its matter (at the molecular level) at distance intervals equal to the smallest possible unit of measure.