We study the effects of Cu substitution in Fe1.1Te, the non-superconducting parent compound of the iron-based superconductor, Fe1+yTe1−xSex, utilizing neutron scattering techniques. It is found that the structural and magnetic transitions, which occur at ∼ 60 K without Cu, are monotonically depressed with increasing Cu content. By 10% Cu for Fe, the structural transition is hardly detectable, and the system becomes a spin glass below 22 K, with a slightly incommensurate ordering wave vector of (0.5-δ, 0, 0.5) with δ being the incommensurability of 0.02, and correlation length of 12Å along the a axis and 9Å along the c axis. With 4% Cu, both transition temperatures are at 41 K, though short-range incommensurate order at (0.42, 0, 0.5) is present at 60 K. With further cooling, the incommensurability decreases linearly with temperature down to 37 K, below which there is a first order transition to a long-range almost-commensurate antiferromagnetic structure. A spin anisotropy gap of 4.5 meV is also observed in this compound. Our results show that the weakly magnetic Cu has large effects on the magnetic correlations; it is suggested that this is caused by the frustration of the exchange interactions between the coupled Fe spins.