Transitive verb for making a blade, point, claw, or similar edge sharp, often by using a whetstone or abrasive. 研ぐ is the usual spelling; 砥ぐ highlights the whetstone/sharpening nuance.
My father sharpened the kitchen knife with a whetstone.
猫が柱で爪を研いでいる。
The cat is sharpening its claws on the post.
2
godan verb (-gu), transitive verb
wash rice
Used specifically for washing rice by rubbing the grains in water before cooking. This sense as especially associated with 磨ぐ, though 米を研ぐ is also a very standard spelling.
Used when rubbing or abrading a surface to clean it, smooth it, or bring out a shine. Compared with 磨く, this often suggests a more abrasive or craft-like process.