Understanding lipid sorting of multicomponent cell membranes associated with tubular deformation is of essential importance to many cell activities such as filopodial growth and protein-mediated vesiculation. Here, we conduct theoretical analysis to investigate how the membrane tubulation induced by an external pulling force over a finite region is regulated by the coupling between the lipid composition and the membrane bending rigidity and tension. It is shown that the presence of the lipid-disordered phase facilitates the nanotube formation by reducing the force barrier. As the pulling region size and the membrane tension increase, the membrane tubulation becomes discontinuous regardless of the coupling effect. The direct proportional relationships between the maximum pulling force and size of pulling region at different coupling scenarios are identified. Analytical solutions for the linear force-extraction relation and the membrane configurations in the early stage of the membrane extraction are obtained. Our results indicate that in the case of a relatively small pulling region, the coupling between the membrane composition and mechanical properties plays an important role in regulating the membrane extraction, and such an effect due to the phase separation diminishes gradually as the pulling region enlarges and the force barrier becomes dominated by a large pulling region.