In this paper, we studied the quasi-two-body Bc → D (s) [ρ(770), ρ(1450), ρ(1700) →]ππ decays by employing the perturbative QCD (PQCD) factorization approach. The two-pion distribution amplitudes Φππ are applied to include the final-state interactions between the pion pair, while the time-like form factors Fπ(w 2 ) associated with the P -wave resonant states ρ(770), ρ(1450) and ρ(1700) are extracted from the experimental data of the e + e − annihilation. We found that: (a) the PQCD predictions for the branching ratios of the quasi-two-body Bc → D (s) [ρ(770), ρ(1450), ρ(1700) →]ππ decays are in the order of 10 −9 to 10 −5 and the direct CP violations around (10 − 40)% in magnitude; (b) the two sets of the large hierarchy R 1a,1b,1c and R 2a,2b,2c for the ratios of the branching ratios of the considered decays are defined and can be understood in the PQCD factorization approach, while the self-consistency between the quasi-two-body and two-body framework for Bc → D (s) [ρ(770) →]ππ and Bc → D (s) ρ( 770) decays are confirmed by our numerical results; (c) taking currently known B(ρ(1450) → ππ) and B(ρ(1700) → ππ) as input, we extracted the theoretical predictions for B(Bc → Dρ(1450)) and B(Bc → Dρ(1700)) from the PQCD predictions for the decay rates of the quasi-two-body decays Bc → D[ρ(1450), ρ(1700) →]ππ. All the PQCD predictions will be tested in the future experiments.