Can I negotiate to leave specific contracts behind even in an asset purchase?

Yes, and this is exactly what an asset purchase is built to allow — nothing forces a buyer to assume a particular contract just because the rest of the business is being sold. The assumed-contracts schedule in the purchase agreement is a negotiated list, and a contract with unfavourable terms, an unwanted counterparty, or one that's simply not useful to you can be left off it.

The nuance is separating what's legally possible from what's practically workable. Leaving a contract behind is straightforward on paper, but if the business's ongoing operations genuinely depend on the relationship it covers — a key supplier, a critical customer, a service provider the business can't easily replace — excluding the contract may just mean you need to negotiate a brand-new agreement with that same counterparty after closing, on whatever terms they're now willing to offer you as a new, unproven customer. Sometimes that's a better outcome than inheriting old terms; sometimes it isn't.

Before deciding to leave a contract behind, it's worth having a business lawyer assess how essential that relationship actually is to the business you're buying, not just whether the contract's terms look unattractive on the page.