Depends a bit on what you want to save.
If it is the resulting video as part of the timeline, then you can produce a selection from the timeline by selecting this section with the yellow arrow-pointers. However, it is only possible to save a part in the time line with all tracks included within the selected start and end time. If you only want to save a cut of one (or more) tracks separately then unless you are able to unselect unwanted tracked before you produce a selection, there do not seem to be other ways.
If you are looking to save a selection on your timeline as a project, then the answer is NO, there is no function for that. What I do in those cases is save the project with a generic name, cut the surrounding and then save the separate bit, with the overall timeline still in place in the saved project. (You can of course all undo the cutting to restore the timeline.
The other way around may also be an option. If you have one or more selections separately saved as projects you can insert these projects as projects on the timeline. That of course should be possible in your workflow and requires some planning ahead.
Hope this is a bit clear. Let us know how you proceed.

Quote Depends a bit on what you want to save.
If it is the resulting video as part of the timeline, then you can produce a selection from the timeline by selecting this section with the yellow arrow-pointers. However, it is only possible to save a part in the time line with all tracks included within the selected start and end time. If you only want to save a cut of one (or more) tracks separately then unless you are able to unselect unwanted tracked before you produce a selection, there do not seem to be other ways.
If you are looking to save a selection on your timeline as a project, then the answer is NO, there is no function for that. What I do in those cases is save the project with a generic name, cut the surrounding and then save the separate bit, with the overall timeline still in place in the saved project. (You can of course all undo the cutting to restore the timeline.
The other way around may also be an option. If you have one or more selections separately saved as projects you can insert these projects as projects on the timeline. That of course should be possible in your workflow and requires some planning ahead.
Hope this is a bit clear. Let us know how you proceed.

Thanks for the reply

Warry
What you described is pretty much what I was doing but it's time consuming and I was hoping that there would be a faster & easier way of doing it.

But thanks for the reply.

It also depends on what you're going to do with the cut sections. If you're going to use them in other PD projects, you may want to use the Precut feature in the Media Library as that will let you place any of the precut sections on the timeline in new projects.

If you need purely standalone clips for use outside of PD, then Warry's suggestions are the way to go. You can save some time by creating all the projects first and then producing them all at once using Batch Produce.