One of the most critical processes in glass machining is laser cleaving using a non-diffracting beam or filamentation. Typically, the cleaving process is based on generating microcracks in a controllable way using a Bessel or other non-diffracting beam. This paper presents the results of ultra-thin glass and laminated UTG cleaving using tailored ultrashort pulses generated by an industrial-grade femtosecond fiber laser. UTG processing is an important and growing application for ultrafast lasers due to the constantly evolving display and consumer electronic market. This specific material requires unique parameter optimization and can be processed in different regimes. A non-diffracting beam was also applied for hybrid polymer-glass and pure polymer samples. This novel approach based on pulses shorter than 300 fs helps to overcome the heat accumulation problem and the low cutting speed of thick polymer substrates. Processing of medical grade polylactide (PLLA) as well as popular PMMA is shown. The applied laser emits a fundamental wavelength of 1030 nm with a pulse duration tunable from 250 fs up to 8 ps. A high-quality cleaving of the UTG, laminated UTG, and the polymer is successfully demonstrated. The influence of pulse duration and pulse pitch on the quality and edge roughness is discussed.