Could astronauts use suction cups during space walks?

It sounds like it might work however they would not be able to climb too high because the higher you go, the less effective a suction cup will be. And in space it's no good at all!

How Suction Cups Work

They work because of air pressure. Air pressure is the weight of the earth's atmosphere pressing on things.

We don't feel the air pressure on us, but that's because it's evenly balanced inside and out. But in fact, there is an atmospheric pressure of 15 pounds per square inch on everything around you, including you.

Earth's Atmosphere And Air Pressure

When you set the suction cup down on a surface, the air pressure is balanced on all sides. Force the air out of the bowl, however, and now the air pressure is all concentrated on one side.

The weight of the earth's atmosphere is actually what holds the cup against a smooth surface!

Not A Good Plan

That's neat in itself, but you may see the problem. Up on top of a high mountain there is less air pressing down, so suction cups won't work as well. Out in space there is no pressure at all. A suction cup wouldn't hold for an instant.