LED Controller Wiring Schematic
That appears to be designed to control standard common-positive RGB LED tape via DMX, so it's not clear where you're getting "SPI control" from.  The V+ connection on each of the output terminal blocks connect to the common positive of the LED tape, and each of the R, G, and B connections connect to the individual negative connections on the tape.

It's not immediately clear how large those terminal blocks are, but at best they're going to be 5.08/5.0mm, and the highest current rating I've seen for that size of terminal is 20A per position.  However, connector current ratings are complicated, and you cannot assume that a rating of 20A for a single position means that you can run 20A on EVERY position in a multiposition connector.  Unfortunately there's no simple answer as to what your actual maximum current rating would be, since this depends on the construction and quality of the connector, the operating environment, and the design of the PCB and enclosure surrounding the connector.  However, I think it's safe to assume that 60A, or 30A per position on that power input connector, is not advisable.

As to why there is a second two-position V- connector, at first glance there's really not a good reason for this.  For some equipment you do want a dedicated low impedance connection to ground either for electromagnetic compatibility (in other words, electrical noise) or for safety, but neither of these is a major issue for a device like this.  Assuming that it's not actually another power input connector with V- and V+ but incorrectly marked, it's probably there specifically because the smaller four-position input connector cannot handle the full 60A the device can theoretically deliver.  

The reason it's only a V- connector in that case is that the device is really only switching the negative side of the various arrays of LEDs--the V+ connection on the output connectors will be directly connected to the V+ on the input connector.  This means that for higher power applications you can connect the positive sides of all of the loads directly to the power supply, bypassing the controller entirely, while leaving the negative sides of the loads connected to the controller outputs.  You will still need to connect the V+ input on the controller to the power supply of course, since it needs its own power to operate as well.

In this arrangement, it's plausible that the connectors themselves would be adequate for the full 60A assuming all of the V- terminals are used, but it's still an open question as to wether the PCB is up to the task.

As a general note, it's not necessarily accurate to use the sum of the output current ratings to determine the total current rating on a device like this.  It's quite reasonable to want to have a higher per-channel rating so you have flexibility in how you allocate your loads even if you can't use the full load rating on all channels simultaneously.