JMP report windows consist of a set of 'display boxes', most of which respond to a right mouse click by showing a context menu. If you right click on a table box, you can select 'Make Into Data Table' to put the same information into a JMP table. Once you have this, you can do 'File > Export' to the format of your choice.
To complement my colleague Ian's recommendation, an alternative approach is to, from the JMP analysis platform report window:
1. Select File -> Save As
2. Select the file type you desire, .txt is one of the available options.
This path will send ALL the report elements to the .txt file and from there you can modify/edit as you see fit.