Mono-Green Deck: Responding to Sorceries/Instants?
The format you're playing is very important to answer this question. Playing Standard, for example, limits your options to the most recent few sets, while on the opposite end of the spectrum, playing Vintage or Commander opens up nearly every card ever printed.

Against removal, you can go for creatures with hexproof/shroud (Thrun, the Last Troll/Scythe Tiger), means to grant hexproof/shroud (Asceticism/Aspect of Mongoose), protection (Chameleon Colossus/Tel-Jilad Defiance), regeneration (Experiment One, Fortitude), indestructible (Predator Ooze, Thornling), etc.

Against countermagic, green is probably the best solution (besides perhaps also playing blue for countering the countermagic); there are a number of cards in green which either can't be countered, or make something else uncounterable. For example, Gaea Herald, Mistcutter Hydra, Savage Summoning.

Against discard and mill, green is probably second only to black in terms of re-using the graveyard. Gensis, Eternal Witness, Creeping Renaissance. Green and black are also the two colors of the Golgari guild, where the extremely powerful Dredge mechanic comes from (which involves self-mill).

Green is also quite good at noncreature removal; in fact, the majority of targeted removal in green is noncreatures only.

With a full card pool, you have a lot of options. For example, I have a mono-green Commander deck (Ezuri, Renegade Leader elf tribal) which often plays like a blue deck, thanks to cards like Ezuri or Wirewood Symbiote protecting my creatures (regenerate or return to hand to protect from removal), Gaea's Herald or Cavern of Souls stopping counterspells, Yeva, Nature&#39;s Herald letting me take "turns" during my opponents' turns, Survival of the Fittest or Fauna Shaman searching for answers to threats (especially with Masked Admirers creating an engine), Sylvan Library drawing cards, etc.