Microwave pulses are used ubiquitously to control and measure qubits fabricated on superconducting circuits. Due to continual environmental coupling, qubits undergo decoherence either when it is free or when it is coupled to an incident pulse. We study theoretically the decoherence-induced effects when a qubit is subject to the driving of time-dependent pulses, which can accomplish geometric logic gating, under a dissipative environment with linear spectral distribution. We find that a transmissible pulse of finite width adopts an asymmetric multi-hump shape, due to the imbalanced pumping and emitting rates of the qubit during inversion when the environment is present. The pulse shape reduces to a solitonic pulse at vanishing dissipation and a pulse train at strong dissipation. We give detailed analysis of the environmental origin from both the perspectives of envelope and phase of the propagating pulse.