  We apply a suitable replica technique to develop a perturbative expression
for the entanglement negativity of bipartite mixed states in
T$\overline{\text{T}}$-deformed CFT$_2$s up to the first order in the
deformation parameter. Utilizing our perturbative construction we compute the
entanglement negativity for various bipartite mixed states involving two
disjoint intervals, two adjacent intervals, and a single interval in a
T$\overline{\text{T}}$-deformed CFT$_2$ at a finite temperature, in the large
central charge limit. Subsequently, we advance appropriate holographic
constructions to compute the entanglement negativity for such bipartite states
in T$\overline{\text{T}}$-deformed thermal CFT$_2$s dual to BTZ black holes in
a finite cut-off bulk geometry and find agreement with the corresponding field
theoretic results in the limit of small deformation parameter.
