Systems and methods for machining openings of a component are provided. In one exemplary aspect, a laser system includes features for machining an opening into a component, such as a cooling hole for a CMC component of a gas turbine engine. The component can be oriented in a first position and lasered while oriented in the first position to form a portion of the opening. The component is then oriented to a second position and lasered while oriented in the second position to form another portion of the opening. The component is alternated between the first and second positions until the predetermined geometry of the opening is formed. The component is oriented in the first and second positions such that the laser beam can machine the component without clipping areas that are not desired to be machined.