With your permission, I'll use your question for the benefit of all of our readers. First, your angelonia is definitely not dead and it’s not about to be either. As a matter of fact, she’s looking great. In a moment I'll explain what is happening to her and what you should do, but before we begin let's try to describe what we’re looking at in the picture. Yours is a beautiful young angelonia planted in a pot intended for indoor use. I assume you know that in order to get the most from your Angelonia, it needs 6 - 8 hours of direct sun daily. It young, but is a strong little plant and it loves fertilizer – but we’ll get to that too.
Now let's prune.
What is happening to your plant is its the natural lifecycle. Blooming ends (nothing is dying here, don't you worry), and what you see now is the seed spreading stage. It is the final stage of the flower’s life cycle. What you should do now is cut and remove those purple-blue dry flower clusters. Just make sure you remove them only after they are dry.
Where to prune exactly - Either directly beneath the dead and dry flower clusters, or a little lower. You don’t need to cut exactly under the dead flower, you can even cut back your angelonia to half size. I've marked the cutting points with orange lines so you can see more or less where to prune.
Fertilize – As I mentioned above, agnolias love fertilizer. And if you choose to use one (liquid or granulated) fertilize a few days after you prune.
Watering – In general, angelonia do benefit from a little dryness from time to time. There's nothing wrong with letting perennials dry out a little, from the color of the soil in the picture, I think yours is a little over watered. Most gardeners treat angelonia as annuals, but this plant is a tough one. Dryness will encourage strong bloom and growth.
Proper watering - Just stop adding water as soon as you see it come out of the drainage holes at the bottom. And check that the soil is dry before watering again.
Container size - Looking at your plant, I do recommend replanting. Putting it in a bigger pot (soon after you've pruned) will give the roots more space to develop.
Other than all said that, enjoy the wonderful plant have there.
I hope that helps. Eyal
Providing general guidelines on 'how to prune' any kind of plant is important, but there are plants, and there is YOUR plant. So despite there being loads of information on this site, I also provide specific and personalized support. If something wasn't clear, or you're not sure of your plant's name, simply send me a picture with your question. Use the form below and I'll get back to you. In the mean time, see what others are asking.