Here are some quick steps you can follow to eliminate the problem of Maya files taking too long to save and also reduce the file size considerably.
• Light Linker Nodes: This is the main reason behind increasing the save time. The cleanUpLightLinker script disconnects all the light linker nodes. You can see the light linker nodes by going to Outliner > Display and check off the DAG Objects Only option. This script only helps if the file is taking too long to save.
• Clear Dead Nodes: After running cleanUpLightLinker script go to the Outliner > Display and check off DAG Objects Only option. Check whether the light linker nodes are present or not. If they are still present you can use the mhClearDeadNodes script to clean those.
• Go to the Hypershade > Edit > Delete Unused Nodes.
• Try deleting all the Non-Deformer History (Edit > Delete All by Type > Non-Deformer History).
• You can delete the blend shape targets if they have been applied to the mesh.