If the Spellcaster you send to the Graveyard for the first part of this card's effect is DARKAttribute, you can simply revive it again with the second part of this card's effect, essentially removing one of your opponent's monsters for free.
Since this card sends the monsters as part of the effect, it can be used with "Shaddoll" monsters to activate their effects.
If you have a "Breaker the Magical Warrior" on your field with no Spell Counter on it and no way to replenish it, by using "Breaker" for this card's requirement, you can easily swap out a weakened, possibly easy prey monster, for a more powerful Spellcaster.
A good time to activate this card is when your opponent Tribute Summons a monster while you control a Spellcaster. You can send both your monster and that Tribute Summoned monster to the Graveyard though this card's effect and replace it with a powerful Spellcaster like "Dark Magician", "Cosmo Queen", and in Traditional Format, "Dark Magician of Chaos", leaving your opponent short one powerhouse and possibly wide open to an attack.
In relation to the above tip, this card is useful against "Monarch" monsters. Since almost all of them require to be Tribute Summoned in order to activate their effects, this card can be used to remove the "Monarch" monster from the field, preventing its ability from activating, while giving you a powerful monster in response.
This card works well as a searcher in "Magician" decks, as by it's very nature it has an abundance of DARKSpellcaster monsters, and can even search for non-Pendulum Magicians of the archetype such as "Tuning Magician".
In relation to the above tip, the "Magician" Pendulum Monsters also make great candidates as the required Spellcaster needed to activate this card. Since Pendulum Monsters don't go to Graveyard when the leave the field, instead returning to the Extra Deck, you essentially get a free monster removal and free powerhouse Spellcaster with no real loss to you, as you can Pendulum Summon them again later.
You can create an interesting combo using this card, "Dark Magician Girl", "Sage's Stone" and "Dark Magician". First, you must have "Sage's Stone in your hand, this card on the field, and a Spellcaster in play. When your opponent summons a monster (preferably and Extra Deck one), activate "Dark Renewal" to send it and your Spellcaster to the Graveyard and summon "Dark Magician Girl". On your next turn, if "Dark Magician Girl" is still on the field, then you can use "Sage's Stone" to summon a "Dark Magician" from the deck, giving you two powerful monsters. Follow that up with cards like "Thousand Knives", "Dark Magic Attack" or, for the biggest impact, "Dark Burning Magic". Even without the other cards, this will ensure that you have two powerful monsters on your field while taking down one of your opponent's monsters in the process.
In general "Dark Magician" decks can heavily benefit from this card, easily enabling them to search/retrieve "Dark Magician", "Dark Magician Girl", or any other DARK Spellcaster for whatever situation it is needed for with no hassle while removing a possible threat at the same time.
"Legion the Fiend Jester" makes an excellent candidate as this card's cost. Not only will you summon a powerful Spellcaster and remove an opposing monster, but you can then search/retrieve another Spellcaster, in this case a Normal Monster, from your deck/Graveyard, granting no real loss in Card advantage.
Use this against "Stardust Dragon" since it doesn't destroy a monster, only sends it to the Graveyard, thereby bypassing "Stardust Dragon's" ability and removing it with no effort.
Use "Witch of the Black Forest" as the required Spellcaster for this card's effect, not only allowing you to Special Summon a Spellcaster, but also search your deck for another monster.