If you reduce the number of ticks on the deer, there are fewer ticks to infect the mice and people. When the deer pick up more ticks from the mice then the tick population is reduced as they visit the 'four poster' stations. The photos of the tick infestation on the deer before and after are pretty dramatic. Pyrethrins are produced by chrysanthemums and have a fairly low toxicity for mammals and birds. Pyrethrins are degraded relatively rapidly by sun and oxygen. There is no free lunch here but keeping deer populations in check and reducing tick infestations are good first steps. The wiki link to pyrethrins and their properties: http://en.wikipedia.org/wiki/Pyrethrin
One further note: ticks laugh as they swim through freshly applied DEET which is an insect repellant NOT a tick repellant. Pyrethrin sprays on external clothing are your best protection if you are in tick infested areas. "Repel Permanone" spray (and similar) is usually available in hardware stores. Lyme is a very serious disease and avoiding it is very important as it can be difficult to diagnose and very difficult to treat especially if you have a reaction to antibiotics.
Last time I put up a link to the best tick puller on the market it was censored so good luck. Current research seems to show getting ticks off within 48 hours is key.
The Connyak BBS