will a new one grow?
The plant has not produced seeds and it appears that two buds are forming further down the stem. I'm assuming this is a sunflower, or a very similar sunflower-esque plant....

I would think you have a sunflower-esque houseplant of which there are many, so go ahead and cut it and see what happens. True sunflowers need more light than you could get from a sunny window unless you augmented it with grow lights. RScott

no because the seeds are in the plant

I have never known a sunflower to do so, inside or out. Has it produced seeds yet? If it has not, there may be a chance since reproduction is a primary aim for plants.

just keep the stalk and see what happens, i have a dope plant as a house plant and have kept it going for 3 years

is the sunflower meant to be a houseplant?

no,dont do it!!! this is murder,we are not allowed to behead in the UK,its only allowed in muslim states.try a more humane way....like bury it up to the neck then stone it. hope this answers your question

No you use the seeds to grow a new plant.