There is no need to Tribute the Spellcaster-Type monster that is required to activate this card. A "Sangan" or a Token would make a suitable Tribute as long as there is a another Spellcaster on the field at the same time.
This card can be used to effectively Summon a high Level Spellcaster-Type monster with 1 Tribute.
This card combos incredibly well with "Mutant Mindmaster". Using the effect of "Mutant Mindmaster" to take control of an opponent's monster and attack with it, one monster your opponent controls can be destroyed. Then, use "Magical Dimension" during that Battle Phase from your hand, and Tribute the stolen monster to Special Summon a Spellcaster and destroy a monster your opponent controls. Essentially, a 2-card combo has allowed yourself to Special Summon any huge Spellcaster and destroy a grand total of 3 opponent's monsters.
This card works well with "Soul Exchange". If your opponent has 2 or more monsters and there is 1 face-up Spellcaster-Type monster on your field, 2 monsters your opponent controls can be rid by Tributing one of their monsters to destroy another one of their monsters. However, your Battle Phase have to be skipped.
This card can also be used to destroy one of your own monsters, like in the case that your opponent gives you a monster that self destructs or is a searcher ("Giant Rat", "Mystic Tomato") (through a card such as "Creature Swap").
A monster can be Tributed to Special Summon "Fortune Lady Light" from your hand, and then destroy it with the additional effect of "Magical Dimension" to activate the effect of "Light".
"Stardust Dragon" can be destroyed easily with this card, since "Stardust Dragon" can't negate it, while getting yourself a new Spellcaster to attack.
Since this card is a Quick-Play Spell Card, it can be used during your opponent's turn. Not only will a strong Spellcaster-Type monster be Summoned, but a weaker monster can be protected (possibly Tributing it for this card's effect), and even destroy an attacking monster, thereby crippling your opponent's strategy and field.
Since "Dark Magician of Chaos" allows yourself to retrieve a Spell Card when it's Summoned, the "Magical Dimension" that was used can be retrieved. After attacking with "Dark Magician of Chaos", use "Magical Dimension" to Summon another Spellcaster and give more damage in same turn or ever finishing your opponent at that point.