Provided are a computer program product, system, and method for reducing a rate at which data is mirrored from a primary server to a secondary server. A determination is made as to whether a processor utilization at a processor managing access to the secondary storage exceeds a utilization threshold. If so, a determination is made as to whether a specified operation at the processor is in progress. A message is sent to the primary server to cause the primary server to reduce a rate at which data is mirrored from the primary server to the secondary server in response to determining that the specified operation is in progress.