How to cut a single clip in a Sequence into multiple clips for use in multiple Sequences in Premiere Pro
Here's the "Premiere" way to do it.  Create N sequences, one for each of the N speakers you want to create an output clip for.  Copy (by reference) the clip into each of the N sequences.  If you do this correctly, you will have N sequences and 1 clip in your project folder.

For each sequence, set the in and out points of the clip to bound the speaker of interest.  Name the sequence according to the speaker.  If you do this correctly, you will still have N sequences and 1 clip in your project folder.

Here's the magic: select all the sequences and hit "Export Media".  This will queue up the creation of N clips.  Each one will be exactly the speaker it should be, and the clip file names will be based on the sequence name (meaning something related to each speaker).

That is how to do it.