Can I demolish or alter my side of a shared wall in a semi-detached home in Ontario?

Not freely, even though it's technically "your side" of the wall. Because a shared wall in a semi-detached home structurally supports both units at once, demolishing or materially altering your side can remove support your neighbour's unit actually depends on, and doing that without their consent, particularly if it causes damage, can expose you to liability under common-law principles even without a formal party wall agreement in place.

This is true whether or not a written agreement exists between the two properties. If there is a party wall agreement, it likely sets out specific notice or consent requirements before either owner can alter the wall, and you'd need to follow those. If there's no agreement, you're still not free to do as you like — the underlying common-law obligation not to damage or endanger your neighbour's support remains; it's just less clearly documented, which tends to make disputes messier rather than giving you more freedom.

Before any renovation that touches a shared wall, such as removing a section or changing an opening, get an engineering assessment and give your neighbour advance notice, and seek their consent where the work could affect their side, rather than assuming your half is entirely yours to do with as you wish.