Some variations provide a system for extracting a product from biomass, comprising: a process chamber having an internal volume; one or more mechanical elements configured to controllably and reversibly mechanically seal the process chamber and reduce the internal volume to mechanically compress the biomass; a fluid port in flow communication with the process chamber; and a collection sub-system in flow communication with the fluid port. Other variations provide a method of extracting a product from biomass, the method comprising: introducing biomass into a process chamber; mechanically sealing the process chamber; mechanically compressing the biomass to release a first fluid material; mechanically decompressing the biomass; introducing an extraction solvent into the process chamber; maintaining process-chamber pressure from about 1 bar to about 1000 bar, wherein the extraction solvent extracts a second fluid material; and recovering the second fluid material from the process chamber. High processing throughput is enabled with this invention.