A compound miter saw is awesome in part because it can easily cut wood on both a horizontal and vertical diagonal (i.e., make mitered cuts). If you take away this capability (such that the saw only cuts straight down), you have a saw that's probably smaller and might cost a little less. What's the common name, referencing the motion used to bring the blade into contact with the wood, for this somewhat less-awesome power tool?
Chop Saw (Cut-Off Saw)