Yata is made of spiritual energy but only someone with Hagoromo's Yin would be able to create it in the first place so it's definitely made of Sage chakra.
Where is this coming from? Itachi has Uchiha Yin chakra, which is descended from Hagoromo, but he does not have Hagoromo's Yin; that belongs to Indra Transmigrants or Hagoromo himself. To my knowledge, we never learned (even in Itachi *******) when or how Itachi obtained the Yata Mirror, so we can't confirm that it in fact was created by Hagoromo.
Further, merely being Hagoromo's Yin does not make something "Sage Chakra" (i.e., Senjutsu formed by combining chakra with Natural Energy). Oftentimes people confuse "Sage Jutsu" (Senjutsu) with the "Sage's Jutsu," due to the obvious similarities of the names, but they are not always the same. Nagato, Edo Madara, pre-Jinchuuriki Obito, and Rinnegan Sasuke all use the "Sage's Jutsu" (using the Rinnegan) and thus use some of Hagoromo's chakra, but none of them were using "Sage Jutsu" (Senjutsu). Madara in particular used the Rinnegan (and thus the "Sage's Jutsu" containing Hagoromo's chakra), both as an old man and as an Edo, but never obtained or experienced Senjutsu until after stealing it from Hashirama.
So in short, the Yata Mirror is not Senjutsu (if that's what you were implying) to render it impervious to being erased by Truth-Seeking Orbs, etc.