Here are the tools I use for pruning roses, from smallest to largest:
1)
Pruning shears: these can tackle anything up to 0.75" (2 cm) diameter. I have the Felco(tm) pruners with unequal handle lengths.
2)
Branch loppers: anything up to approx. 1.25" (3.5 cm) diameter. Keep the blades sharpened.
3)
Pruning saw: mine cuts on the push *and* the pull stroke, and I use it for anything larger than 1.25" but still within my strength. Example: I used the pruning saw on my MIL's fig tree in early March to cut a lateral branch approx. 2" (5 cm) in diameter. I might have been able to deal with as much as 3" (7.5 cm) across, but anything larger than that would have needed power tools, and I don't have the hand strength or the shoulder stability to wield power tools at shoulder level, which is where these branches were.
[url=https://www.organicrosecare.org/index.php]This[/url] is a site on organic rose care, to help with "kicking the chemical habit" (if you've been treating your roses chemically). Organic rose care generally costs much less, both in terms of time and money, than chemical rose care.
[url=https://www.ars.org/?page_id=3175]This[/url] is a one-page summary of "pruning principles" from the American Rose Society (ARS).
Please don't use an "axe" on a rose bush, no matter how overgrown. Roses need clean cuts on their canes so they won't invite insects, disease, and other undesirables to invade their beautiful selves.

Use the pruning shears this year and, next year, perhaps have an experienced rose grower advise you in person with heavier-duty tools at the ready.
If the bushes are as densely overgrown as I'm imagining, keep this overriding guideline in mind:
*never* remove more than one-third of a plant in one season ("season" = spring to winter in this sense). The plant can go into shock and die.
If you need to remove more than one-third of the plant, then plan your removals over more than one season. Some trees and larger shrubs need to be planned for a three-year take-down in order to save the plant and not send it into shock.
Cynthia H.