Hospital Wing
Answer: NOSES
Each of these phrases consists of a word followed by an "amputated" version of that word. The missing letters spell out the solution phrase.
despot's raving = TYRANT RANT
painting of a diagram or table = CHART ART
egg-shaped hole = OVOID VOID
parasite in a woman's garment = BLOUSE LOUSE
plate of crunchy roots = RADISH DISH
dirt in the floor of a fireplace = HEARTH EARTH
manor's condition = ESTATE STATE
poem praising negative terminal of a galvanic cell = ANODE ODE
Noah's boat, at night = DARK ARK
indistinct fever = VAGUE AGUE
scent manufacturing plant = OLFACTORY FACTORY
pizza boy's uniform = DELIVERY LIVERY
blunt weapon expert = MACE ACE
air pollutant area = OZONE ZONE
Aragorn's ire = RANGER ANGER
gangsta embrace = THUG HUG
terse hyperbola or ellipse = LACONIC CONIC
cowardly black bird = CRAVEN RAVEN
child's instinct = KID ID
why the mutiny happened = TREASON REASON
boundary of a row of shrubs = HEDGE EDGE
duct for an occasion = EVENT VENT
moral tale that can be split into parts = SEPARABLE PARABLE
The chopped-off letters spell out TYCHO BRAHE AND VOLDEMORT LACK THESE, which clues the answer NOSES.