Two words crossing

The clues on the left give these:

An X:

ACROSS (A cross)

A II:

TWO

A 10:

ANX (An X)

Behind:

DOWN

Not an other:

ONE

Not a head:

BEHIND

Next ...

Roughly preserving the layout, and replacing cardinal numerals with corresponding numbers, we have a proper set of crossword clues for the right side crossword:

  $\small\underline{\text{ACROSS}}$
  2. An X
  $\small\underline{\text{DOWN}}$
  1. Behind

to which the answers are   ACROSS   and   DOWN   respectively.

which of course makes sense.
Thanks TSL denizens for the right final words, though the reasoning to get there gets a little twisted -

Each group of clues on the left has a clue that is also an answer to a different clue.
  "An X" yields "Across", but is also the answer to "A 10".
  "Behind" yields "Down", but is also the answer to "Not a head".
The final clues, "An X" and "Behind", just give their left-side answers as their right-side answers.

Completed puzzle, courtesy of OP:

Partial Answer:

I'm not sure what to do with the right side as yet, but here's what I've got for the left.

An X:

LETTER

A II:

TWO

A 10:

TEN

Behind:

BACK

Not an other:

Not sure

Not a head:

BEHIND