The adjective for "mutate" is "mutable", and not "mutatable". I wonder why the last two letters (-te) have been removed before adding "-able" to the end of it. Is there any rule? Any similar adjectives?
Good question. The reason has to do with the fact that the verb mutate was a back-formation from the noun mutation. That is, the English noun mutation existed first, and the verb mutate was invented later to match it.
Both came ultimately from the Latin mutare (to change form) and mutatio (a change).
I'm not sure, but the "correct" way to do this might have been to create the verb mute.
Unfortunately, mute (myoot) already existed in English, meaning "silent"(adj) / "to silence" (v). It has a separate derivation:
Latin — mutis
Old French — mu
French — muet
English —mute http://i.word.com/idictionary/mute
And moot also already existed in English, with quite a distinct meaning (related to "meet") from Germanic origins. http://i.word.com/idictionary/moot
So it seems the solution taken was to adopt the Latin-sounding mutate as the verb form, to avoid confusion with moot or mute.
But mutable came fairly directly from Latin mutabilis. (This did not collide with existing English, because apparently mutable, in the sense of silenceable, did not exist in English (or if it ever did, that meaning disappeared long ago; it is not listed in, for instance, Merriam-Webster—not even as archaic.)) http://i.word.com/idictionary/mutable
There are a bunch of rules how adjectives ending with -able are formed. And yes, one of them is that silent 'e's are dropped, which would support your expectation of mutate -> mutatable.
However, there is another rule that deals with verbs ending with -ate:
Traditionally, verbs ending in -ate drop this suffix before adding -able; hence,
- communicable (“able to be communicated”),
- eradicable (“possible to eradicate”),
- implacable (“unable to be placated”),
- inimitable (“unable to imitated”), and so on,
- but relatable, because relate is re- + -late, not rel- + -ate.
Logically one should therefore say rotable to mean "able to be rotated", but rotatable has become accepted.
Your mutable falls squarely in this category.
The adjective existed already in Latin mutabilis/mutabile, from the verb mutare. So English mutable is not derived from English to mutate, but has the original Latin form.
As a matter of fact, there is no general rule for forming adjectives. However, when you use the suffix able to form adjectives from the verbs that end with "tate", you usually omit the last three letters "ate" and use the suffix "able".
Some examples are as follows:
Agtitate - agitable
Irritate - irritable
Imitate - imitable
mutate - mutable