Step 1: Understand peptide bond formation.
A peptide bond is formed between two amino acids.
The carboxyl group \((-\mathrm{COOH})\) of one amino acid reacts with the amino group \((-\mathrm{NH_2})\) of another amino acid.
Step 2: Identify the eliminated groups.
During this reaction:
\[
-\mathrm{OH}
\]
comes from the carboxyl group and
\[
-\mathrm{H}
\]
comes from the amino group.
These combine together to form water.
Step 3: Write the reaction.
\[
\mathrm{R-COOH+H_2N-R'\rightarrow R-CONH-R'+H_2O}
\]
The linkage \((-\mathrm{CONH}-)\) formed is called the peptide bond.
Step 4: Eliminate incorrect options.
\(\mathrm{NH_3}\), \(\mathrm{CH_3OH}\), and \(\mathrm{CO_2}\) are not released during peptide bond formation.
Step 5: Final conclusion.
Hence, the molecule eliminated during peptide bond formation is
\[
\boxed{\mathrm{H_2O}}
\]