Meanings
This idiom refers to a drowning man grabbing any floating object, even a straw, to save himself. It was first used by Thomas More in A Dialogue of Comfort Against Tribulation (1534).
How to pronounce "grasp at straws":
AU
To guess randomly or pursue any apparent option, due to a lack of clear choices or information.
To get hold of any help, even if it is insignificant.