Which river is called muddy river of USA

The correct answer is Missouri. The Missouri River is often called the "Big Muddy" due to the large amount of silt and sediment it carries. It is the longest river in North America and a major tributary of the Mississippi River. Its muddy appearance comes from the erosion of the Great Plains and the Missouri River Valley.

The Mississippi is large but not specifically known as the "muddy river," and the Rio Grande and Yukon are not associated with this nickname.