The other answers (and the manual) cover what you can/can't do. As far as why:
Resistance is measured by trying to send a small current through the item being tested. That requires electrical contact with two points on an item.
As I understand it, alternating current can be measured without direct contact because of the relationship between a changing magnetic field and a changing electric current. That is how (essentially) transformers work, which is arguably (there was a lot more to it...) the main reason why AC won the war of the currents - you can easily build transformers to convert AC between high voltage for transmission and low voltage for (relatively) safe residential use. So a clamp (or any other non-contact method) can't easily measure direct current.
It is possible to measure voltage (as with current, AC and not DC) in a non-contact method. Electric meters, beyond the basic residential models, use CTs (Current Transformers) and PTs (Potential (i.e., voltage) Transformers) to turn things like 100A @ 14,400V into 1A @ 120V, which is then measured by a meter and multiplied by the CT and PT ratios to produce the reported values. My hunch is that there just isn't that much need for clamp voltage measuring in a typical residential/small building environment because the voltages are (a) relatively safe (120V and 240V, occasionally higher but almost always well under the magical value of 600V) (b) usually no need to measure in a contact-less way. If you think you have a voltage problem (e.g., lost neutral), you just use the probes directly in receptacles or in the panel.
On the other hand, clamp current metering is very handy as it lets you test an item while it is being used - e.g., to measure the current on an active circuit or even on an entire panel (clamp around one of the feeder wires). Clamp reading, as with other types of non-contact measurement devices (e.g., a non-contact voltage tester, which this particular meter can also do using the clamp but which is typically found as a small separate tool), is safer for the user (no exposure to conductive materials), safer for the measurement tool (any current within the range of typical residential values instead of limiting to 10A) and generally avoids influencing the circuit under test.
In addition, this particular meter doesn't even have a way to measure current using the probes, and many that do (e.g., my Klein) have a relatively low limit when using the probes to measure current such as 10A - not even enough to measure a basic 15A circuit safely.