SPI Half-Duplex for the Holtic HI-3593 ARINC429 IC
SPI is logically a circular buffer - I mention this as you seem confused.

On page 14 of the datasheet (behind a script), it states:


  In the general case, both master and slave simultaneously send and receive serial data (full duplex), per Figure 5 below. However the HI-3593 operates half duplex, maintaining high impedance on the SO output, except when actually transmitting serial data. When the HI-3593 is sending data on SO during read operations, activity on its SI input is ignored. Figures 6 and 7 show actual
  behavior for the HI-3593 SO output.


This is not unusual at all (and just about every Holt device I have used that has SPI does this); During command transmit, the SO pin will not be driven at all (the slave SO pin is High-Z); i.e. there is no meaningful data at the host receive pin.

This expands on a comment; to read data, operate the clock normally; and data on SI at the HI-3593 is ignored.