Could we use some kind of rotating sling or magnetic loop to accelerate a spaceship to (very) high speed and then release it and hurl it away?

Today all spaceships are propelled by engines and some fuel/energy source on board themselves. An alternative concept which has been proposed is to put the engine and fuel at or near Earth, and beam the propulsive power to the spaceship. The basic advantage would be that literally all resources in our world would be available for it, instead of only the "luggage" which we can put on the spaceship itself.

But wouldn't it, in principle, be even better to accelerate the spaceship before we launch it? Speed doesn't weigh down the payload.