Laser-based fabrication can be an alternative technology to mechanical grinding and polishing processes. However, the performance of these elements in real applications still needs to be validated. In this paper, we demonstrate that the subtractive fabrication technology is able to produce high-quality axicons from fused silica, which can be efficiently used for glass processing. We comprehensively investigate axicons, fabricated by ultrashort pulsed laser ablation with subsequent CO2 laser polishing, and compare their performance with commercially available axicons. We show that laser-fabricated axicons are comparable in quality with a precision commercial axicon. Furthermore, we demonstrate the intra-volume glass modification and dicing, utilising mJ-level laser pulses. We show that the tilting operation of the laser-fabricated axicons results in the formation of directional transverse cracks, which significantly enhance the 1 mm-thick glass dicing process.