Hold down Shift to move a part along the X and Z axes.
Hold down Ctrl/CMD to move a part along the Y axis.
If you move a part too far from whatever it's attached to, it will become parentless and Spore will class it as non-existent.
The larger a part is, the further it needs to be from the parent part to become parentless.
https://1drv.ms/u/s!AvuubHYsSlZUmkvUPzw ... Z?e=xPv4P9
Outdated versions, for archival purposes: