In short, because the table is a control, you'll need to use a local and write an empty string array to it.
The button should be latched (right click on it on the front panel and select mechanical action->latched until released) and wired to a case. Right click on the table on the diagramme and select create local. Place the local inside the true case. Right click on the local and select create constant, and wire that constant to the local. If the clear operation needs to be done at a specific time (you want to read the table just prior to reading the button click e.g.) make sure the data flow ensures this.
