Yes, you can decrease your tax burden by suffering business losses. The only expenses you'd be claiming would be actual spending you do. So, if you spend $100 in advertising and have $0 revenue, you have $100 in losses which saves money on taxes but costs you money in total.
The exception to this is home office expense, since you are already paying rent. If you portion out some of your dwelling and use it for business exclusively, you could save on taxes without additional spending. Similarly the portion of utilities associated to your home office can be deducted.
It is acceptable to have losses year over year, but if audited you'd have to prove that you are intending to make money (profit motive) and not just trying to dodge taxes (tax fraud). If you aren't running a legitimate business that happens to lose money, then you are likely to have losses disallowed and/or face penalties.
I would suggest you focus on using a side business to make more money rather than viewing it as a way to save on taxes. The IRS can easily sniff out attempts to dodge taxes, so make sure it's a legitimate business endeavor. Keep separate financial records, and research allowable business expenses thoroughly to make sure you have a defensible position in case of audit.
Here's a handy IRS article on Deducting Business Expenses