I Cannot Afford Any Tattoo Removal Procedure. What's my Safest At-Home Removal Option?

The only safe and effective practice to remove tattoos is to see an expert with the latest technology laser.  For patients who can not afford tattoo removal here options:
Try a payment plan and space out your treatment sessions.  If a tattoo session is $200 and you finance it over 6 months, it is less than a haircut. 
Once your tattoo is light enough, either tattoo over your existing tattoo with skin color ink or have another tattoo placed over it.
Wear skin camouflage make up to help conceal it.
Try and cover with clothing (not possible for all tattoos)

Do not let a friend cut out a tattoo on your body. The risks could be fatal from severe infection and the scarring could be disfiguring.

Tattoos can be made to fade significantly, but scarring is inevitable, from salabrasion which was a sailor’s way in the olden days to rub raw the skin and as it healed, the tattoo pigment would be pushed up through the raw eroded skin and the color lightened.  Then after healing it would be done and repeated several times. Infection could occur. Not the entire tattoo would be eliminated, often, leaving a “ghost” of the tattoo behind.

Dermabrasion with a sterile diamond wheel does the same as salabrasion. Neither of these procedures should be done by non professionals as the risk of infection could be high and lead to serious consequences. If financial limitations exist, it may be possible to seek care by a university-based dermatology practice that has a teaching clinic that offers discounted procedures but no one should take this into their own hands and risk serious complications which could even be fatal.

The information provided in Dr. Shelton's answer is for educational purposes only and is not intended to constitute medical advice.  The information provided should not be relied upon as a substitute for consultations with a qualified health professional who may be familiar with your individual medical needs. 

Unfortunately, I cannot offer you any advice as to how to remove the tattoo aside from laser. Microdermabrasian or "sanding" does not penetrate deep enough to remove a tattoo, even when done in a physicians office. Excising the tattoo is not a reasonable option, even if it was done by a plastic surgeon, as the neck contains lots of vasculature, and may not heal well with scarring. Not to mention, doing any of these options at home leaves the risk of bleeding and infection. The best option would be to consult a physician for a series of laser treatments. You could always speak with their medical care coordinator about a payment plan or opening up a CareCredit (medical credit card) account. Best of luck to you.