If you want it to produce lower pitchers, than you would have to cut it down to a stump.But don't worry, it'll grow back.I'm not sure if it'll grow plantlets but most nepenthes do.I started with one nepenthes sanguinea and now I have 5!!.
- Adrian

Next to my plant is a stump that was cut off when I received it.

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As you can see there is one living leaf, but also two blackish-gray parts where it was cut off. I wonder if this portion of the plant will begin to grow again. Thoughts?

Sorry to keep adding on to my post, but this pic is from the other side of the plant. A plantlet maybe? Pic is a bit blurry, but not too bad.

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Oh yeah,
I see it.It is hard to tell if it is a plant or a one of it's baby leaves.
And that little stump, since the top is black it will not grow anymore.
- Adrian

What if I cut it down a bit more there?

I'm not sure but if you do, and it looks fresh and green then it might grow back.
If I were you I would try that because that little plant will produce nice lower pitchers.But only cut it down until you get to a green part.
- Adrian

Here's a picture of the ex-stump. It looks pretty green and juicy. Any idea on how long it will take before I see some new growth? Picture

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OK,
Now all you have to do is wait a couple of weeks and you will see tiny leaves sprouting out of the stump.If you want to speed it up then you would have to take it out of the pot and dip the stump in rooting hormone.And remember to mist the stump alot or it'll turn black again.
- Adrian

Or, you could just leave the plant alone for a while and it will grow new vines with younger base leaves that will grow lower pitchers. If you take a cutting from the plant's upper vine, it will make a new plant with only upper pitchers... If you cut the plant down, it would have to start the process over again and make lower pitchers like Carnivorousplants indicated. Since it is a new plant, why stress it more now? It looks great to me.

Give Sarr NW a call and explain the situation. They may have some suggetsions

I would not drastically prune your Nepenthes. Nepenthes do not have tuberous storage roots, and if you cut off most of the growing stem, your plant will be very slow to recover. It will be like starting over with a small cutting. Your plant will sprout new basal rosettes in time, and if you leave the existing stem, new growth will be much faster. When the basal rosettes are large enough, you can prune off the climbing stem without setting back your plant.

If you allow the climbing stem to droop below the level of the pot, that will often induce the plant to produce a new basal rosette with lower pitchers.

Ive heard basal shoots at the beggining grow a little lower pitchers