The mushroom industry should implement green extraction technologies; however, there is not enough information on the differences between these techniques expressed as the chemical composition of the resulting extract. In this study, selected types of green extraction techniques (GETs) were used on Chaga (Inonotus obliquus) (Fr.) Pilát from Serbia (IS) and Mongolia (IM) to examine the differences that would enable the composition-based technology choices in the mushroom supplement industry. Subcritical water extraction (SWE), microwave-assisted (MW) extraction, and ultrasonic-assisted extraction (VAE) were used to prepare the extracts. SWE was performed at two different temperatures (120 and 200 °C), while 96% ethanol, 50% ethanol, and water were used for MW and VAE. The yield, the content of total phenols, total proteins, and carbohydrates, qualitative and quantitative analysis of phenolic compounds, carbohydrates, including α- and β- and total glucans, and fatty acids, were determined in the obtained extracts. SWE resulted in a significantly higher yield, total polysaccharide, and glucan content than any other technique. Glucose was the most dominant monosaccharide in the SWE samples, especially those extracted at 200 °C. The MW 50% EtOH extracts showed the highest yield of total phenols. Among the tested phenolic compounds, chlorogenic acid was the most dominant. SWE can be recommended as the most efficient method for extracting commercially important compounds, especially glucans and phenols.