It sounds like you are saving remotely or it is backing up remotely over the Internet probably to iCloud.
Saving over a slow network connection is obviously going to be a lot slower than just saving to your fast internal Hard Drive.
The problem is multiplied when you have a large file with lots of large images and you are also using Time Machine which takes time to make its backups as well.
It is also possible you are approaching the capacity of your Hard Drive. OSX likes to have 15-20% free to write its temporary files to the hard drive. The less room for the writes, the longer it takes to find empty spots and your compiter can appear to slow down dramatically.