Swoop! Teleporter has many uses, some of which may not be intuitive at first glance.
Keep in mind the restriction on Swoop! Teleporter: both Pokémon must be Basics, and cannot be ex's.
The most obvious use for Swoop is as a Pokémon Trader for Basics: you trade away one of your Basics for another that is more useful. For example:
You can Swoop away your starting Pokémon for a Jirachi or any other Basic that helps you set up.
If you have an Evolution in hand but the wrong Basics in play, you can Swoop one of them away for the right Basic.
Some Evolutions are very powerful, but their reputation precedes them — if you play their Basic forms, your opponent might make it a priority to go after them. They may not even be safe on the Bench, as spread damage attacks, Pow! Hand Extension, and Pokémon Reversal exist. Swoop can help get the Evolution in play without exposing the Basic to a KO:
You can Swoop away a Basic (that has already been in play for a turn) for Voltorb, evolve to Electrode ex, and use Extra Energy Bomb, all without giving your opponent a turn to interrupt this sequence.
If your opponent has a Pokémon-ex Active, you can put a Safeguard Wobuffet in front of it and start building up Energy on the Wobbuffet. When the time is right, you Swoop Wobbuffet away for the Basic form of your main attacker, evolve it, and start beating down. This is effective as Wobbuffet forces your opponent to warp their plays around it — if you put the Basic up against the ex, your opponent would just attach Energy on their ex and KO your Basic, but when you put Wobbuffet up against the ex, your opponent will attach Energy to one of their Benched Pokémon that can deal with Wobbuffet instead, ideally a Pokémon that loses the 1v1 against your Evolved attacker.
Note that this works because the new Pokémon inherits the old Pokémon's "has already been in play for 1 turn" characteristic, and hence can be evolved immediately.
This trick was mentioned in the Choosing Basics section: you can Swoop away a high HP Pokémon with damage on it for a low HP one in order to KO the new Pokémon and feed your opponent a Prize, turning on your (or turning off your opponent's) Pow! Hand Extension, Scramble Energy, etc.
Some Basics can end up being liabilities, typically as bait for Pow! Hand Extension or Pokémon Reversal, or by accruing damage from Cursed Stone while on the Bench. Swoop can be used to get rid of them:
You can Swoop Jirachi, Lapras, or other setup Pokémon away after they've fulfilled their purposes. (Note that you still need a Basic to replace them with; if you fail to find with Swoop, the old Pokémon stays where it is.)
Suppose your Lapras got Pow-ed Active and retreating it would take too long. You can get rid of it by Swooping it away for something with a lower Retreat Cost (or something that evolves into one), something that will be KOed by the damage counters on it, or a Voltorb that you then evolve into Electrode ex and blow up.
If your deck plays tech Basics, and you've already identified that one of them will be useless in the current matchup, you can deliberately Holon Mentor for it, Bench it, and Swoop it away for what you actually want. This removes the dead draw Basic from your deck.
You can Swoop away a Pokémon with a when-played Power (e.g. Lapras) for something else, then use Pokémon Retriever or Holon Farmer to recycle it and use its Power again.