Was that trade even really blocked by the Ottomans if they were trading on a massive scale themselves, and they were often in friendly relations with many European powers? Most notably France, but Commonwealth was also often on good terms with Ottomans, England and Netherlands had no reasons to fight them, and even Italian states traded with them all the time. Besides, Atlantic caravel expeditions began way before the Ottoman conquest of Egypt (1519) which would be required to truly "cut off trade with Asia" (which brings back the original question, why would Mamluks trade but not Ottomans - the former brutally fought crusades, the latter were allied to France).
Absolutely right, and I should clarify.
The Spice Trade was what drove the Indian Ocean sea trade between Indonesia, south India, Sri Lanka, southern Arabia and Egypt.
After Rome fell out of it in the 5th century CE, Arab and Indonesian sailors took over, but the market for luxury goods like spices in western Europe flat-lined - the trade was all with Byzantium/Constantinople and the Middle East. By the time western Europe was a decent market again, after the 8th - 9th centuries CE, the trade across the Mediterranean was dominated by the Italian City States, especially Venice, Genoa, and to a lesser extent Pisa, Ancona, and Ragusa.
As stated, the Italians traded extensively with Caliphate, later Ottoman, Egyptian and southern Arabia tribes. The problem was, they held a monopoly at the selling end in Europe, and as sea trade developed after 1000 CE in northern and western Europe, the non-Italians increasingly wanted to break that monopoly and get their hands directly on the enormous profits to be made. As they developed ships with better long-distance capabilities, like the Portuguese Ballingers (the direct ancestors of the Caravels) Portugal took the lead in expeditions down the African coast, 'around' the direct Mediterranean routes dominated by the Venetians and Genoese.
I should have made it clear, the problem was not conflict with the Arab/Ottoman world or polities, but with the European 'Middle-men' in Italy. The original European historians' assumption was that it was part of the Christian-Islamic conflicts, but that has been thoroughly debunked by, among others, Braudel's research into Mediterranean trade in the late middle ages. The internal conflict (among 'Christian' states) continued as Portugal got around Africa first and started (no later than 1507 CE) a concerted effort to gain an absolute monopoly on Indian Ocean trade that would, basically, cut off traffic through the Mediterranean completely before the goods even got there. That led the Spanish to look for alternatives, which led directly to financing Columbus' cross-Atlantic voyage(s).
The fact remains, it was the search for alternatives to the 'old' routes of trade through the middle east (especially from southern Arabia and Egypt) and across the Mediterranean that led to the development of longer-range sailing and cross-ocean exploration by Europeans. Without the goal of major profits to be made from that trade, the expeditions never would have been funded.
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