Both are somewhat correct, but it's better to use simplest. This is called the superlative in grammar. It can be used by either adding the word "most" before the adjective, or by modifying the adjective with the suffix "-est". If you care about the rules, here is a quote from oxforddictionaries.com:
The superlative is formed in different ways according to the length of
the base adjective. If it has one syllable, then the letters -est are
added. If the word has three syllables or more then the word most is
placed before the adjective: most attractive. Words of two syllables
vary: some add -est and some use most. Some even do either, for
example clever. Spelling: adding -est If the word ends in a consonant,
add -est (quick becomes quickest). Words of one syllable with a short
vowel sound and ending with a single consonant, double the consonant
and add -est (sad becomes saddest). With words of one syllable ending
in ‘l’, you normally do not double the ‘l’, but cruel becomes
cruellest. If it ends in ‘e’, add -st (late becomes latest). If it
ends in ‘y’, change the ‘y’ to an ‘i’ and add -est (happy becomes
happiest).
emphasis mine. Also, if you look it up in the dictionary (e.g. here), you will see "simple - simpler - simplest".
More than that, Simplest is also used more often that "most simple", you can see a clear tendency at this ngram (Sorry, it's small when added here as a picture. The blue line is "simplest", and the red line is "most simple"):
It is pronounced as \ˈsim-p(ə-)ləst\
, so you can pronounce it either with 3 syllables, or just 2 if you omit the first ə
.
Most has two closely-related meanings.
1 the largest in number or amount
2 more than half / almost all of somebody/something
As that OALD link says, the most is often used for the first meaning - but informally, the is often omitted. It's never used with the second meaning.
Suppose The Queen of Hearts were to ask "Who ate my tarts?"...
A1: "The knave ate the most"
A2: "The knave ate most"
If several courtiers ate one tart each, but the knave ate two, then either answer could validly be given, since he ate more than anyone else (but note that A1 is a "very slightly formal" usage).
But if the knave actually ate more than half (but not all) of the tarts, only A2 is correct. Though the Queen might not understand that intended distinction, since the could be omitted anyway.
It's worth making the point that the is never included when most simply means very...
"I am most grateful for your help"
...but interestingly, whereas in...
"There were 50 people there, at [the] most"
... the is normally omitted, it's almost always included if we add very as an intensifier...
"There were 50 people there, at the very most"
Best Answer
Most monosyllabic (1-syllable) adjectives seem to use -er/-est to form superlatives.
Most trisyllabic (3 syllables) or longer adjectives seem to use the "more/most" construction.
According to various grammar sites, there's no clear rule for bisyllabic adjectives, with some suggesting checking the dictionary to see if -er and -est forms are listed immediately after the root word (but I don't think that's great advice because one can publish a more consolidated dictionary by just leaving those forms out).
In this specific case, "most tragic" is clearly correct and "tragicest" isn't, but I have a hard time explaining any rule why, beyond deference to a dictionary. The best I can offer by way of a generalizable test is this Ngram which shows "most tragic" in reasonably common use and "tragicest" not found in the millions of books Google indexed. That strategy can be used to figure out which superlative form other adjectives typically take.