In Cypress.io is there anyway to control the test run?

I don't know if there's a way to do it from the user interface, but you can use mocha methods to run only chosen tests by:

1. Replacing it with xit tests you want to omit
2. Using it.skip on tests you want to omit
3. Using it.only on single test you want to run

To skip entire context/describe suite use context.skip() or describe.skip() which are identical.

Use it.only() and it.skip()

See cypress documentation: https://docs.cypress.io/guides/core-concepts/writing-and-organizing-tests.html#Excluding-and-Including-Tests