Despite the continuing research interests in CNT-liquid systems, the microscopic structure and transport behavior of liquid mixtures in carbon nanotubes (CNTs) remain poorly understood. Methanol and water liquids are completely miscible across the entire range of concentration; however, recent research reveals that they are immiscible at a molecular level. In this work, we carried out classical molecular dynamics to study the molecular distribution, structure ordering, clustering and transport behavior of liquid methanol-water mixtures within CNT confinement. We found that CNTs preferentially absorbed methanol over water molecule even though the latter has a smaller molecular size, indicating that chemical effect such as molecular hydrophilicity plays a crucial role in the molecular absorption of CNTs. Due to the selective absorption of CNTs, methanol aqueous solution changes from microscopically immiscible to macroscopically immiscible at nanoscale. This nanoscale immiscibility may be utilized in various applications of CNTs including direct methanol fuel cells, nanosensors, molecular sieves, nanofluidic chips, and capsules for drug delivery.