I want to save JSON request and response in shared drive using groovy script.

Thorough not sure how you are currently saving the requests and responses, you could map or mount the shared location to your drive and use that.
For example //shared/data can be mapped to local z / y drive(it can be any name) and write there what is the issue unless the location is hard coded. You can use a project property for the location as it can change on computer.

Another approach can be write a batch script to copy once execution is completed.