Generally, cutting the cord means canceling your cable (or satellite) service. But, that may not be the way to go. You may want to simply "trim" the cord, not fully cut it.
For some people, the option to downgrade their television service is a viable option. Many cable providers offer a low-cost "Locals Only" package. They don't promote these heavily, but locals only packages are often available. You many need to search extensively on your cable provider's Website to find information about it. Or, a visit to the local cable office may be in order.
Why would you do this? Well, depending on your location, terrain, and other factors, it may be expensive to put up an antenna that is sufficient to receive the over-the-air channels you want. You can either do without, or pay your cable company for local channels only.
If your cable provider is also your Internet provider, you may get a bundle discount, even on such a small bundle. For many, it's easier and more convenient to pay a small amount, usually in the $10/month range, for a locals-only package than to deal with work or cost of putting up an antenna.
Many DVRs, including TiVo work well with cable systems. Click here to find out more about TiVo.
One final benefit of a locals-only package is the ability to authenticate against your account on certain streaming apps. Read more about that here.