DRUMMER CAFE

I think you will loose the bass tone.

The narrow neck and upper chamber act as a spring thus making much deeper sounds  (bass) irrelevant of the drumhead size. Thus one gets three tones, edge, tone(1/3) and bass (center).

while (let say 16") frame drum has just two edge and tone.  hitting it in the middle like djembe won't give a bass tone.
if you would add a neck to a frame drum you would get a djembe/doumbek like bass tone.

The throat of the drum, which is the part you are talking about removing, is what gives the drum it's low-end.  In fact, a wide neck on one of these drums (including a ceramic doumbek) will have LESS low-end than the narrow neck versions. It's this funnel shape that helps to build up the bottom frequencies that our ears perceive.

I've never done what you are proposing, but based on other drums that I've played as well as what I've studied in regards to the physics of sound ... this drum would sound very dry ... little resonance with a short decay time.

I'm curious as to what (even why) you are attempting here. Are you bored or just curious?  

I sure would hate to see a nice drum ruined by cutting off the throat. I imagine that if you keep a little bit of the neck of the drum, as your picture shows after the pruning, you may not loose as much as what I think you will. It will DEFINITELY be different ... if not drastically different.

The depth of ANY drum increases the potential for deeper ptiches and/or low-end frequencies to be realized. Take an octabon for example. They all have a 6-inch diameter head, but the shell depth helps to create the realized pitch differences.

You'll get some low-end from your reduced drum ... but it's not going to be anything like what it used to be prior to the surgery.