Step 1: Define the effect.
The $(-)\mathrm{R}$ (negative resonance) effect means a group pulls $\pi$ electron density away from a conjugated system into itself.
Step 2: State the structural signature.
Electron-withdrawing-by-resonance groups carry a multiple bond to an electronegative atom, such as $\mathrm{C=O}$, $\mathrm{C \equiv N}$ or $\mathrm{-NO_2}$.
Step 3: Examine $-\mathrm{COOR}$.
The ester carries a polarised $\mathrm{C=O}$; its $\pi$ electrons shift toward the carbonyl oxygen, draining density from the attached system. This is a clear $(-)\mathrm{R}$ group.
Step 4: Examine $-\mathrm{OR}$ and $-\mathrm{OH}$.
Both have oxygen lone pairs that they push into the conjugated system, giving a $(+)\mathrm{R}$ donating effect.
Step 5: Examine $-\mathrm{NHR}$.
The nitrogen lone pair is likewise donated into conjugation, again a $(+)\mathrm{R}$ effect.
Step 6: Conclude.
Only $-\mathrm{COOR}$ withdraws by resonance, so it shows the $(-)\mathrm{R}$ effect, option (A).
\[ \boxed{-\mathrm{COOR}} \]