Premiere: Make clips from extracts of same clip
You can create subclips of the sequences in the source material that you want to use seperately. This will create a second instance of the source material in the Project Panel that is limited to a specific part of the source. A subclip is sort of a virtual copy of the original clip (the source material on the disk is not copied).

To create a subclip, you first have to set In- and Out-Points. The subclip will use those as boundaries, so only the part between them will be available in the subclip. 

You can set In- and Out-Points at the current playhead position using the I- and O-keys. After you have set those points for the active clip in the Source Panel, right-click on the clip in the Project Panel and select Make Subclip. You can then set a name for the subclip, after that it's available in the Project Panel.

You can also edit your subclips after you created them, which is useful if you realize you need a longer part of the sequence after you created the subclip. The Edit Subclip option is available from the context menu as well, you can shift the start/end timecodes of the supclip this way. There's also an option to restrict the sequence to the subclip's boundaries, which is active by default, you might want to turn it off depending on your workflow.