No.  The top figures show projections of two trefoil knots, each of which can be assigned a different (or same) crossings.  Join the different assignments in the different crossings, as shown at the bottom to get two different knots, not related by a mirror reflection.

After all, one can be the un-knot (loop) and another a true knot, and these cannot be related by a mirror symmetry (of course).

[![enter image description here][1]][1]

  [1]: https://i.sstatic.net/ePBLP.png