Can caffeine be separated from coffee?
Yes, this is how decaffeinated coffee is made. If I recall correctly, this is done commercially by dissolving the caffeine in dichloromethane (DCM), or more recently in supercritical carbon dioxide. This switch is probably over concerns regarding chronic industrial exposure to DCM, which is mildly toxic.

From personal experience, I have extracted caffeine from instant coffee using a separatory funnel with a system of water and dichloromethane. Purification by sublimation finished the job.