suppose an astronaut in outer space suddenly discovers hat the tether connecting her to the space?

use the same motion you'd use when your swimming to get back to the shuttle. But i'm sure they have some sort of "jet pack" on their suit that prevents this from happening.

If she tied a bit of rope
to a wrench.......I think theres hope
she must quickly throw away the tool
towards the ship would be the rule
now ......if she pulls along the cord
she d find herself soon back on board..!!

Newton can help.  For every action there is an equal and opposite reaction.

By throwing the tools in the direction opposite the shuttle, the reaction of the tools acceleration would be toward the shuttle.  Since the astronaut is providing the action of accelerating the tool she must absorb the reaction and would be accelerated toward the shuttle.

In the real world, she would get on comm link, call the shuttle and it would either go get her, use the arm to retrieve her or send another astronaut out either on a tether or a MMU (Manned Maneuvering Unit) to retrieve her.

Personally I like the real world better, the odds of getting back by throwing tools is pretty slim.  The slightest misdirection of the throw could complicate matters severely.

Cheers

GIMP

Throw the tools in the direction away from the shuttle, along the line that passes through both you and the shuttle.