Hi
In a sense you can do what you want....
Load your big clip to VP media list.
Method 1....In the clip preview window (left pane) use the IN/OUT markers to isolate the first section you want.
Click the green down arrow to add your selection to the timeline
Method 2...Drag your clip to the timeline and edit it the normal way, leaving the section you want to retain.
Now click the + to the right of "Sequence 1 x"
This clears the timeline and the preview pane and puts your selection into the Sequence bin of the media list.
Click the main clip again on the media list to renew it in the preview pane (even if it still seems to be there)
Repeat the procedure each time for your second and subsequent main clip selections.
If you review your sequence bin in the media list you will see that you have your clips (now called sequence 1; sequence 2 etc.
You can treat these as separate and individual clips..i.e. add them to the timeline; cut and edit them etc.
As you seem to have got all your clips on the sequence line by cutting the main one on the sequence line several times, you may have to start again using the method I have outlined above.
Nat