Let's evaluate each option:

Option A: "Autotrophic organisms classified under Kingdom Monera, Cyanobacteria, are a group of autotrophic organisms classified under Kingdom Monera."

Cyanobacteria are indeed autotrophic (they perform photosynthesis) and are traditionally classified under Kingdom Monera in older taxonomy systems. This statement is correct.

Option B: "Bacteria are exclusively heterotrophic organisms."

This is incorrect because many bacteria, such as cyanobacteria, are autotrophic (capable of producing their own food via photosynthesis) in addition to heterotrophic species.

Option C: "Slime moulds are saprophytic organisms classified under Kingdom Monera."

Slime molds are not classified under Kingdom Monera. They are generally placed in the Kingdom Protista (or Amoebozoa) and are not bacteria.

Option D: "Mycoplasma have DNA, ribosome and cell wall."

Mycoplasma do have DNA and ribosomes, but they lack a cell wall. They only have a cell membrane.

Based on these evaluations, the correct statement is:

$\textbf{Option A}$

This option accurately describes cyanobacteria as autotrophic organisms within Kingdom Monera.