Space debris is also known as space junk, Space garbage and many other names that describe something unimportant. The space is filled with millions of space debris. I cannot categorically say space debris has led to the destruction of satellites before. But I can tell you, it has the capacity to destroy already launched satellites depending on the size of the space debris and how heavy it is.
A small piece of space debris can damage a spacecraft because of it's speed and the nature of collision with the spacecraft. A space debris can be as large as a discarded rocket stage or as small as a microscopic chip of paint. For example, in 2010, when India destroyed a satellite leading to a total number of space debris in the atmosphere. However, the destruction and the pieces of space debris generated did not have effect on any nearby satellite because it's altitude was very below other existing satellites.
India's decision to destroy the satellite could have resulted into the destruction of other satellites provided they are at the same altitude.